Guide to Tables in the Theory of Numbers (1941)

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n BIBLIOGRAPHY M. ALLIAUME. li. Tables jusqu'a «=1200 des Factorielles nl Dtcompostes en Facteurs Premiers et en Factorielles Premieres, Louvain, 1928, 481 p. [e2, 13-481.] Libraries: MiU, NN, RPB l2. Also in Louvain, Universite, Laboratoire d'Astronomie et de Geodesie, Publications, v. 5, no. 56, 1929, p. 1-380 (identical with the same pages above); v. 6, no. 61,1930, p. 101-201 (identical with p. 381-481 above). M. R. ANDERSON 1. Representation as a Sum of Multiples of Polygonal Numbers (Diss. Chi- cago), Chicago, 1936, ii+54 p. [q3.] Libraries: CU, CaM, CaTU, CoU, CtY, DLC, ICJ, ICU, IU, IaU, MdBJ, MCM, MiU, MnU, MoU, NjP, NN, NNC, NcD, OCU, OU, PU, RPB, TxU, WU H. ANJEMA. 1. Table des Diviseurs de tous Nombres depuis 1 jusqu'd 10 000, Leyden, 1767, 302 p. [d.] In the same year there were also editions with prefaces and title-pages in Dutch, German, and Latin. Libraries: MiU, NN, RPB R. C. ARCHIBALD. 1. "Mersenne's numbers," Scripta Math., v. 3, 1935, p. 112-119. [a: C2.] F. ARNDT. 1. "Untersuchungen iiber einigeunbestimmte Gleichungen zweiten Grades und iiber die Verwandlung der Quadratwurzel aus einem Bruche in einen Kettenbruch," Archiv Math. Phys., v. 12, 1849, p. 211-276. [j», 249-276.] 2. "Beitrage zur Theorie der quadratischen Formen," Archiv Math. Phys., v. 15, 1850, p. 429-478. [J2*, 476-478.] 3. "Tabellarische Berechnung der reducirten binaren kubischen Formen und Klassification derselben fiir alle successiven negativen Determi- nanten ( — D) von Z> = 3 bis D=2000," Archiv Math. Phys., v. 31, 1858, p. 335-448. [n, 351-448.] R. J. BACKLUND. 1. "(Jber die Differenzen zwischen den Zahlen die zu den « ersten Prim- zahlen teilerfremd sind," Suomen Tiedeakatemia, Helsingfors, Toim- ituksia (Annales), s.A., v. 32, no. 2, 1929, p. 1-9. [bi.] E. BAHIER. 1. Recherche Methodique et Proprints des Triangles Rectangles en Nombres [85]

BAK-BEE BIBLIOGRAPHY Entiers, Paris, 1916, vii+266 p. [j8, 255-261.) Libraries: ICU, IU, NjP, PU, RPB, TxU, WU F. E. BAKER. 1. A Contribution to the Waring Problem for Cubic Functions (Diss. Chi- cago), Chicago, 1934, ii+39 p. [q3.] Libraries: CU, CaM, CaTU, CoU, CtY, DLC, ICJ, ICU, IEN, IU, laU, MdBJ, MH, MiU, MnU, MoU, NjP, NN, NNC, OCU, OU, PU, RPB, TxU, WU A. S. BANG. 1. "Om tal af formen an+bm — cm,n Matematisk Tidsskrift, B, 1935, p. 49- 59. [k, 57-58.] E. BARBETTE. 1. Les Sommes de piima Puissances Distinctes Igales a une piime Puissance, Li6ge, 1910,154 p.+app. [b7, app.] Libraries: ICJ, IU, MH, NjP, PU P. BARLOW. 1. New Mathematical Tables, London, 1814, lxi+336 p. [ef, 1-167.] Libraries: CPT, CaM, CaTU, CoU, CtY, DLC, IEN, MB, MCM, MH, MiU, NhD, NNC, RPB N. G. W. H. BEEGER 1. "Quelques remarques sur les congruences rf~i= 1 (mod />2) et (p— 1) ! = -1 (mod />2)," Messenger Math., v. 43, p. 72-84, 1913. [d4*, 77-83.] 2. "On the congruence (p — l)l= — 1 (mod />2)," Messenger Math., v. 49, p. 177-178, 1920. [b4*, 178.] 3. "On a new case of the congruence 2"~i = l (mod />2)," Messenger Math., v. 51, p. 149-150, 1922. [b4:d2.] 4. "On the congruence 2P~i=1. (mod />2) and Fermat's last theorem," Messenger Math., v. 55, p. 17-26, 1925. [b4, 18-25: d2, 18-25.] 5i. Additions and Corrections to "Binomial Factorisations" by A. J. Cunning- ham, Amsterdam, 1933, 12 p. [e2.] Hectographed copy. Libraries: RPB 52. Reprint in revised form by the London Mathematical Society: Supple- ment to Binomial Factorisations by the late Lt.-Col. Allan J. C. Cunning- ham, R.E. Vols. I to IX, London, 1933, 12 p. Libraries: RPB 6. "On some numbers of the form 6ks+l," Annals of Math., s. 2, v. 36, 1935, p. 373-375. [%.] 7. "Report on some calculations of prime numbers," Nieuw Archief v. Wiskunde, s. 2, v. 20,1939, p. 48-50. [b4: f,.] 8. "On the congruence 2J>-i==1 (mod />*) and Fermat's last theorem," Nieuw Archief v. Wiskunde, s. 2, v. 20, 1939, p. 51-54. [b4, 53-54: d,, 53-54.] 9. Primes between 61 621 560 and 61 711 650 and between 999 999 001 and 1 000 119 119. Manuscript in possession of the author. [ft.] [86]

BIBLIOGRAPHY BEL-BID E. T. BELL. 1. "Class number and the form xy+yz+zx," Tdhoku Math. Jti., v. 19, 1921, p. 103-116. [n, 116.] J. L. BELL. 1. "Chains of congruences for the numerators and denominators of the Bernoulli numbers," Annals of Math., s. 2, v. 29, 1927, p. 109-112. [h.] G. BELLAVITIS. 1. "Sulla risoluzione delle congruenze numeriche, e sulle tavole che danno i logaritmi (indicf) degli interi rispetto ai vari moduli," R. Accad. Naz. d. Lincei, Cl. d. sci.fis., mat. e nat., Memorie, s. 3, v. 1, 1877, p. 778-800. [c, 790-794: p, 796-800.] A. A. BENNETT. 1. "The four term Diophantine arccotangent relation," Annals of Math., s. 2,v. 27,1925, p. 21-24. [1.] 2. "Table of quadratic residues," Annals of Math., s. 2, v. 27,1926, p. 349- 356. [i2, 350-356.] 3. "Consecutive quadratic residues," Am. Math. So., Bull., v. 32, 1926, p. 283-284. [i2, 284.] G. T. BENNETT. 1. "On the residues of powers of numbers for any composite modulus real or complex," Royal So. London, Phil. Trans., v. 184A, 1893, p. 189-336. [p, 298-336.] M. BERTELSEN, see GRAM 2. W. E. H. BERWICK. [See also MATHEWS 2.] 1. Integral Bases (Cambridge Tracts no. 22), Cambridge, 1927. 95 p. [d4, 68.] Libraries: CPT, CU, CaM, CaTU, CoU, CtY, DLC, ICJ, TEN, IU, laAS, laU, MdBJ, MCM, MH, MiU, MoU, NhD, NjP, NN, NNC, NRU, NcD, OCU, OU, PEL, RPB, TxU, WU C. E. BICKMORE. [See also CAYLEY 6.] 1. "On the numerical factors of a"—1," Messenger Math., v. 25, p. 1-44, 1895. [e2*, 43-44.] 2. "Sur les fractions decimales periodiques," Nouv. Annales d. Math., s. 3, v. I5, 1896, p. 222-227. [e2*, 224-227.] C. E. BICKMORE and O. WESTERN. 1. "A table of complex prime factors in the field of 8th roots of unity," Messenger Math., v. 41, p. 52-64, 1911. [jt, 56-64: p, 56-64.] D. BlDDLE. 1. "On factorization," Messenger Math., v. 28, p. 116-149, 1898-9. [g, 134- 147: h, 134-147.] [87]

BIL-BUR BIBLIOGRAPHY K. K. BILEVICH, see DELONE, SOUINSKII and BILEVICH. G. BILLING. 1. "Beitrage zur arithmetischen Theorie der ebenen kubischen Kurven vom Geschlecht ems," K. Vetenskaps Societeten i Upsala, Nova Acta, s. 4, v. 11, no. 1, 1938, 165 p. (also with special title page, diss. Upsala). [1, 159-163.] G. BlSCONCINI. 1. "Soluzioni razionali delle equazioni indeterminate di tipo xl+i," Periodico d. Mat., s. 3, v. 4, 1907, p. 28-32. [j,, 31-32.] E. BORISOV. 1. O Privedenii polozhitel'nykh trolnichnykh kvadratichnykh form po sposobu Sellinga, s prilozheniem tablitsy privedennykh form dlia vsiekh opredie- liteleJ ot 1 do 200. [On the reduction of positive ternary quadratic forms by Selling's method, with an appended table of reduced forms for all determinants from 1 to 200] (Master's Diss. St. Petersburg), St. Peters- burg, 1890, 108 + tables, 116 p. [n*, 35-116, tables.] Libraries: RPB H. BORK. 1. Periodische Dezimalbruche, Berlin 1895, 41 p. [df, 36-41.] Libraries: IU, MH, RPB C. A. BRETSCHNEIDER. 1. "Tafel der pythagoraischen Dreiecke," Archiv Math. Phys., v. 1, 1841, p. 96-101. [j,, 97-99.] 2. "Zerlegung der Zahlen bis 4100 in Biquadrate," Jn. f. d. reine u. angew. Math., v. 46, 1853, p. 1-28. [q3*, 3-12.] O. BRUNNER. 1 . Losungseigenschaften der Kubischen Diophantischen Gleichung z3 — y2 = D, (Diss. Zurich), Zurich, 1933, 91 p. [1, 83-89.] Libraries: CtY, DLC, IU, NNC, RPB, WU J. C. BURCKHARDT. 1. Table des Diviseurs pour Tous les Nombres du Premier Million, ou plus exactement, depuis 1 d 1 020 000, avec les nombres premiers qui s'y trou- vent, Paris, 1817, viii+114 p. [d,, 114: 6i.]* Libraries: CU, CtY, MH, NN, NNC, RPB 2. Table des Diviseurs pour Tous les Nombres du Deuxieme Million, ou plus exactement, depuis 1 020 000 d, 2 028 000, avec les nombres premiers qui s'ytrouvent, Paris, 1814, 112 p. [BI*.] Libraries: CU, CtY, laAS, MH, NN, NNC, OCU, RPB 3. Table des Diviseurs pour Tous les Nombres du Troisieme Million, ou plus exactement, depuis 2 028 000 a 3 036 000, avec les nombres premiers qui s'ytrouvent, Paris, 1816, 112 p. [ei*.] Libraries: CU, CtY, laAS, MH, NN, NNC, RPB [88]

BIBLIOGRAPHY BUT-CAU P. BTJTTEL. 1. "(Jber die Reste der Potenzen der Zahlen," Archiv Math. Phys., v. 26, 1856, p. 241-266. [ds, 250-253: i2, 244-246.] E. CAHEN. 1. Elements de la Theorie des Nombres, Paris, 1900, xii+408 p. [di*, 375- 390: d3*, 375-390: fi, 370-374: i3*, 391-400.] Libraries: CU, CaM, CaTU, CoU, CtY, ICJ, ICU, IEN, IU, InU, MdBJ, MB, MCM, MH, MiU, MnU, NhD, NjP, NNC, NcD, OCU, OU, PEL, PU, WU 2. Theorie des Nombres, v. 1, Paris, 1914, xii+408 p. [d, 378-381.] Libraries: CPT, CU, CaM, CaTU, CoU, CtY, DLC, ICJ, ICU, IEN, IU, laAS, KyU, MdBJ, MCM, MH, MiU, MoU, NjP, NN, NNC, NcD, OCU, OU, PEL, PU, RPB, TxU, WU 3. Theorie des Nombres, v. 2, Paris, 1924, x+736 p. [di*, 55-56: d3*, 39-54: i3*, 380-382: ji, 267: n, 588-590.] Libraries: CPT, CU, CaM, CaTU, CoU, CtY, DLC, ICJ, ICU, IEN, IU, laAS, KyU, MdBJ, MCM, MiU, MoU, NjP, NN, NNC, NcD, OCU, OU, PEL, PU, RPB, TxU, WU G. CANTOR. 1. "Verification jusqu'a 1000 du theoreme empirique de Goldbach," Ass. Franc, pour 1'Avan. d. Sci., Comptes Rendus, v. 23, pt. 2, 1894, p. 117- 134. [qs, 117-134.] F. S. CAREY. 1. "Notes on the division of the circle," Quarterly Jn. Math., v. 26, 1893, p. 322-371. [0,367-371.] R. D. CARMICHAEL. 1. "A table of multiply perfect numbers," Am. Math. So., Bull., v. 13, 1907, p. 383-386. [a, 385-386.] 2. "A table of the values of m corresponding to given values of <t>(m)," Am. Jn. Math., v. 30, 1908, p. 394-400. [th*.] R. D. CARMICHAEL and T. E. MASON. 1. "Note on multiply perfect numbers, including a table of 204 new ones and the 47 others previously published," Indiana Acad. Sci., Proc., v. 21, 1911, p. 257-270. [a, 260-270.] G. S. CARR. 1. Synopsis of Elementary Results in Pure Mathematics, London, 1886, xxxvii+935 p. [d, 7-29.] Libraries: CPT, CU, CaTU, CoU, CtY, DLC, ICJ, ICU, InU, laAS, IaU(1880), MB, MH, MiU, MnU, MoU, NhD, NIC, NNC, NcD, PEL, PU, WU A. CAUCHY. 1i. "Memoire sur diverses formules relatives a 1'algebre et a la theorie des nombres," Inst. d. France, Acad. d. Sci., Comptes Rendus, v. 12, 1841, p. 813-846. [bi, 846.] 12. Oeuvres, Paris, s. 1, v. 6, 1888, p. 113-146. [bi, 145.] Libraries: CPT, CU, CaM, CaTU, CoU, CtY, DLC, ICJ, ICU, IEN, IU, InU, laAS, [89]

CAY-CHA BIBLIOGRAPHY IaU, KyU, MdBJ, MB, MCM, MH, MiU, MnU, NhD, NjP, NN, NNC, NRU, NcD, OCU, OU, PU, RPB, TxU, WvU, WU 2i. "Memoire sur la resolution des equations indeterminees du premier degre en nombres entiers," Exercises d'Analyse et de Physique Mathe- matique, v. 2, 1841, p. 1-40. [bi, 36-40.] Libraries: CPT, CU, CtY, ICU, IU, laAS, IaU(1840), MB, MH, MnU, NhD, NN, NNC, OCU, RPB 22. Oeuvres, s. 2, v. 12, 1916, p. 9-47. [bi, 43-47.] Libraries: CPT, CU, CaTU, CoU, CtY, DLC, ICU, IEN, IU, InU, laAS, IaU, KyU, MdBJ, MB, MCM, MH, MiU, MnU, NhD, NjP, NN, NNC, NRU, NcD, OCU, OU, PU, RPB, TxU, WvU, WU A. CAYLEY. li. "Note sur 1'equation x*-Dy*= ±4, D = 5 (mod 8)," Jn. f. d. reine u. angew. Math., v. 53, 1857, p. 369-371. [ji, 371.] l». Collected Mathematical Papers, Cambridge, v. 4, 1891, p. 40-42. \jf, 42.] 2i. "Tables des formes quadratiques binaires pour les determinants negatifs depuis D= — 1 jusqu'a D= —100, pour les determinants positifs non Carre's depuis D=2 jusqu'a J9 = 99 et pour les treize determinants negatifs irreguliers qui se trouvent dans le premier millier,"/«./. d. reine u. angew. Math., v. 60, 1862, p. 357-372. [n, 360-372.] 22. Collected Mathematical Papers, v. 5, 1892, p. 141-156. [n*, 144-156.] 3i. "Tables of the binary cubic forms for the negative determinants =0 (mod 4), from —4 to —400; and =1 (mod 4), from —3 to —99; and for five irregular negative determinants," Quarterly Jn. Math., v. 11, 1871, p. 246-261. [n, 251-261.] 32. Collected Mathematical Papers, v. 8, 1895, p. 51-64. [n, 55-64.] 4i. "Specimen of a literal table of binary quantics, otherwise a partition table," Am. Jn. Math., v. 4,1881, p. 248-255. foi, 251-255.] 42. Collected Mathematical Papers, v. 11, 1896, p. 357-364. [qi, 360-364.] 5i. "Non-unitary partition tables," Am. Jn. Math., v. 7, 1885, p. 57-58. [q.-l 5t. Collected Mathematical Papers, v. 12, 1897, p. 273-274. [qi.] 6i. "Report of a committee appointed for the purpose of carrying on the tables connected with the pellian equation from the point where its work was left by Degen in 1817," Br. Ass. Adv. Sci., Report, 1893, p. 73- 120. [ji, 75-119: jt, 75-80: m, 75-119.]* 62. Collected Mathematical Papers, v. 13, 1897, p. 430-467. [ji, 434-466: j2, 434-441: m, 434-441, 443-466.] Libraries (for v. 4, 5, 8, 11, 12, 13): CPT, CU, CaM, CaTU, CtY, DLC, ICJ, ICU, IU, laAS, IaU, MdBJ, MB, MCM, MH, MiU, MnU, MoU, NhD, NjP, NN, NNC, NRU, NcD, OCU, OU, PU, RPB, WvU, WU 7i. "Report of the committee ... on mathematical tables" [theory of num- bers], Br. Ass. Ad. Sci., Report, 1875, p. 305-336. 7». Collected Mathematical Papers, v. 9, p. 461-499. E. M. CHANDLER. 1. Waring's Theorem for Fourth Powers (Diss. Chicago), Chicago, 1933, iv+62 p. [qs, 12-61.] [90]

BIBLIOGRAPHY CHA-COR Libraries: CU, CtY, DLC, ICJ, ICU, IEN, IU, laU, MH, MiU, MoU, NjP, NN, NNC, NcD, OCU, OU, PU, RPB, TxU, WU L. CHARVE. 1. "Table des formes quadratiques quaternaires positives rdduites dont le determinant est egal ou inferieur a 20," Inst. d. France, Acad. d. Sci., Comptes Rendus, v. 96,1883, p. 773-775. [n.] P. L. CHEBYSHEV. li. "Surles formes quadratiques," Jn. d. Math., s. 1, v. 16,1851, p. 257-282. [if, 273-274: n, 273-274.] 12. Oeuvres, St. Petersburg, v. 1, 1899, p. 73-96. [i3, 88-89: n, 88-89.] Libraries: CU, CaM, CtY, DLC, ICJ, ICU, IU, laAS, MdBJ, MCM, MH, MiU, MnU (1907)uNhD, NjP, NN, NNC, NcD, OCU, PU, RPB, TxU, WU 2i. Teorila Sravnenit [Theory of Congruences], (Diss. St. Petersburg), St. Petersburg, 1849, ix+iv+281 p. [d,, 235-264: d3*, 235-264:is*,265-279.] Libraries: RPB 22. Second ed., St. Petersburg, 1879, viii+iii+iii+223+app. 26 p. [di, app. 3-18: ds, app. 3-18: is, app. 19-26.] Libraries: CU, ICJ, ICU, MH, MoU, NN 23. Third ed., St. Petersburg, 1901, xvi+279 p. [di, 235-264: d3, 235-264: i,, 265-279.] Libraries: RPB 24. Theorie der Congruenzen, German transl. by H. SCHAPIRA, Berlin, 1889, xviii+314+app. 32 p. [di, app. 6-21: d3*, app. 6-21: if, app. 22-31.] Libraries: CU, CtY, DLC, ICU, IU, laU, MdBJ, MH, MiU, NhD, NjP, NNC, OU, RPB, WU 28. Teoria delle Congruenze, Italian transl. by I. MASSARINI, Rome, 1895, xvi+295 p. [di, 248-287: ds*, 248-287: i3*, 288-295.] Libraries: IU, RPB L. CHERNAC. 1. Cribrum Arithmeticum, sive Tabula, continens Numeros Primos a com- positis segregatos, occurrentes in Serie numerorum ab unitate progre- dientium, usque ad decies centena millia, et ultra haec, ad viginti millia (1 020 000). Numeris compositis per 2, 3, 5, non dividuis, adscripti sunt divisores simplices, non minimi tantum, sed omnino omnes, Deventer, 1811,xxi+1020p. [d*.] Libraries: CtY, MH, MiU, NN, RPB I. CHOWLA. 1. "The representation of a positive integer as a sum of squares of primes," Indian Acad. Sci., Proc., sect. A, v. 1, 1935, p. 451-453. [fi, 453.] A. E. COOPER. 1. "Tables of quadratic forms," Annals of Math., s. 2, v. 26, 1925, p. 309- 316. [n.] J. G. VAN DER CORPTJT. 1. "Tafel der primitiven gleichschenkligen Dreiecke mit rationalenWinkel- [91]

CRE-CUN BIBLIOGRAPHY halbierenden und mit Schenkeln kleiner als 160 000," Akad. v. Wetensch., Amsterdam, Proc.,afdeeling natuurkunde,v.35, 1932, p. 51- 54. [j,, 52-53.] T. G. CREAK, see CUNNINGHAM and CREAK, CUNNINGHAM, WOODALL and CREAK. A. L. CRELLE. 1. "Table des racines primitives etc. pour les nombres premiers depuis 3 jusqu'a 101, precedee d'une note sur le calcul de cette table," Jn. f. d. reine u. angew. Math., v. 9, 1832, p. 27-53. [di*, 52-53, d2, 36-51: d4, 36-51 :d6, 36-51.] 2. Encykhpddische Darstellung der Theorie der Zahlen und einiger anderer damit in Verbindung stehender analytischer Gegenstdnde zur Beforderung und allgemeineren Verbreitung des Studiums der Zahlenlehre durch den ojfentlichen und Selbst-Unterricht elementar und leicht fasslich iiorgetragen, v. 1 [no more publ.], Berlin, 1845, xxvi+387 p. [di», 387: d2, 371-386: d4, 371-386: d6, 371-386.] Pages 1-368 of this work are mainly reprinted from Jn. f. d. reine u. angew. Math., v. 27-29. Libraries: CtY, MB, MH, NN, RPB 3. "Tafel der kleinsten positiven Werthe von xi und x% in der ganzzahligen Gleichung aixi=atxi-\-l, " Jn. j. d. reine u. angew. Math., v. 42, 1851, p. 299-313. [bi, 304-313: h, 304-313.] J. CULLEN, see CUNNINGHAM and CULLEN. A. J. C. CUNNINGHAM. 1. "On finding factors," Messenger Math., v. 20, p. 37-45, 1890. [i2, 40.] 2. "On 2 as a 16-ic residue," London Math. So., Proc., s. 1, v. 27, p. 85-122, 1896. [d6, 118-122.] 3. [High primes], London Math. So., Proc., s. 1, v. 28, p. 377-379, 1897. [f,, 378.] 4. A Binary Canon, London, 1900, viii + 172 p. [d2, 172: d3*, 1-171.] Libraries: CaTU, CtY, DLC, IU, MdBJ, MB, MH, NNC, RPB, VVU 5. "Period-lengths of circulates," Messenger Math., v. 29, p. 145-179, 1900. [b4, 166-179: d4, 166-179.]* 6. "High primes /> = 4o>+l and 6w+l, and factorisations," Quarterly Jn. Math., v. 35, 1903, p. 10-21. [f2, 19-21.] 7. Quadratic Partitions, London, 1904, xxiii+266 p. [e2*, 1-256: fi, 1-256: f2, 1-256: ji, 260-266: j,*, 1-259.] Libraries: CU, CoU, CtY, DLC, ICU, IU, MdBJ, MB, MH, NNC, RPB, WU 8. "On high Pellian factorisations," Messenger Math., v. 35, p. 166-185, 1906. [e,, 185.] 9. "Evidence of Goldbach's theorem," Messenger Math., v. 36, p. 17-30, 1906. [q,, 29-30.] 10. "High quartan factorisations and primes," Messenger Math., v. 36, p. 145-174, 1907. [f,*, 168-174.] [92]

BIBLIOGRAPHY CUN 11. "On hyper-even numbers and on Fermat's numbers," London Math. So., Proc., s. 2, v. 5, 1907, p. 237-274. [d,, 268-274.] 12. "On binal fractions," Math. Gazette, v. 4, 1908, p. 259-267. [c, 266-267.] 13. "High sextan factorisations," Messenger Math., v. 39, p. 33-63, 97-128, 1909. [i2, 58-63, 125-128.] 14. "Number of primes of given linear forms," London Math. So., Proc., s. 2, v. 10, 1911, p. 249-253. [f5, 251.] 15. "fiquation indeterminee," L'Intermediaire d. Math., v. 18, 1911, p. 45- 46. [1.] 16. "Determination of successive high primes (fourth paper)," Messenger Math., v. 41, p. 1-16, 1911. [fi.] 17. "On quasi-Mersennian numbers," Messenger Math., v. 41, p. 119-146, 1911-12. [e2, 143-145:f2, 144.] 18. "On tertial, quintal, etc. fractions," Math. Gazette, v. 6, 1911, p. 63-67, 108-116. [c, 110-116.] 19. "On Mersenne numbers," Int. Congress Mathems., Cambridge, 1912, Proc., Cambridge, 1912, p. 385. [e2.] 20. [Note on large primes], Sphinx Oedipe, v. 8, 1913, p. 95. [fi.] 21. "Factorisation of N=(y* + 2) and (2/+1)," Messenger Math., v. 43, p. 34-57,1913. [d4, 52-53: e2, 53-57.] 22. "Roots (y) of y"°+1 =0 (mod />*)," Messenger Math., v. 43, p. 148-163, 1914. [d4, 156-163.] 23. "On the number of primes of same residuacity," London Math. So., Proc., s. 2, v. 13, 1913, p. 258-272. [d6, 265-272: f,, 264.] 24. "Factorisation of 7V=(j«+l) and (x'v + y**)," Messenger Math., v. 45, p. 49-75, 1915. [d4, 66: et, 72-74: o*, 57.] 25. "Factorisation of N=(xv + y)," Messenger Math., v. 45, p. 185-192. 1916. [e2, 190-192.] 26. "Factorisation oi N & N'=(xn^yn)-^-(x^y), &c. [when x—y=l]," Messenger Math., v. 49, p. 1-36, 1919. [e2, 23-30.] 27. "Factorisation of xn±y" etc., when x — y = n," Messenger Math., v. 52, p. 1-34, 1922. [e2, 28-34.] 28. Binomial Factorisations, v. 1, London, 1923, xcvi+288 p. [d4, 1-95: es, 97-236: ft, 1-95, 237-288: h, 1-21: j,, 185-194:1, 229-236.]* Libraries: CU, CtY, ICU, IU, NjP, NN, NNC, PU, RPB, WU 29. Binomial Factorisations, v. 4 [Supplement to v. 1], London, 1923, vi+160 p. [d4*: f,*: ii, 1-18.] Libraries: CU, CtY, ICU, IU, NjP, NN, NNC, PU, RPB, WU 30. Binomial Factorisations, v. 2, London, 1924, lxxix+215 p. [d<, 1-104: e,, 105-199: f,, 1-104, 201-214.]* Libraries: CU, CtY, ICU, IU, MH, NjP, NN, NNC, RPB, WU 31. Binomial Factorisations, v. 6 [Supplement to v. 2], London, 1924, 103 p. [d4: f,.]* Libraries: CU, CtY, ICU, IU, MH, NjP, NN, NNC, RPB, WU 32. Binomial Factorisations, v. 3, London, 1924, lxix+203 p. [d«, 1-152: e2, 153-195: f,, 1-152, 196-203.]* Libraries: CU, CtY, ICU, IU, NjP, NN, NNC, RPB, WU [93]

CUN BIBLIOGRAPHY 33. Binomial Factorisations, v. 5, London, 1924, lxxii+120 p. [d4, 1-101: e2, 103-118: f2, 1-101, 119, 120.]* Libraries: CU, CtY, ICU, IU, NjP, NN, NNC, RPB, WU 34. Binomial Factorisations, v. 7 [Supplement to v. 3, 5], London, 1925, 117p.[d4:f».] Libraries: CU, ICU, IU, NjP, NN, NNC, RPB, WU 35. "Determination of successive high primes (fifth paper)," Messenger Math., v. 54, p. 1-19, 1924. [ei, 8-19: f,*f 5-7.] 36. Quadratic and Linear Tables, London, 1927, xii+170 p. [d6, 125-133: e,, 1-87, 162-170: fi, 1-87: f,, 1-87: g, ii:h, 134-161: ii, 90-92, 96-99, 103-123: i2, 89, 93-95, 100-102: i3, 124: J2, 1-87.] Libraries: CU, CtY, ICU, IU, NjP, PU, RPB 37. "Factorisation of y"Tl, b>12]," Messenger Math., v. 57, p. 72-80, 1927. [e,*, 75-80.] 38. Binomial Factorisations, v. 8, London, 1927, iv+237 p. [d*: f2.]* Libraries: CU, ICU, NjP, RPB 39. Binomial Factorisations, v. 9, London, 1929, vii+167 p. [d4: fi.] Libraries: CU, RPB 40. "On Haupt-exponent tables," Messenger Math., v. 33, 1904, p. 145-155: v. 34, 1904, p. 31. 41. (a) "Factor-tables. Errata," (b) "Quadratic partition tables.—Errata," Messenger Math., (a) v. 34, p. 24-31, 1904; v. 35, p. 24, 1905; (b) v. 34, p. 132-136, 1905. 42. "Theory of numbers tables—errata," Messenger Math., v. 46, 1916, p. 49-69. A. J. C. CUNNINGHAM and T. G. CREAK. 1. Fundamental Congruence Solutions Giving One Root (£) of Every Congru- ence yl=-\-l (mod p and pk) for All Primes and Powers of Primes <10 000, London, 1923, xviii+92 p. [d4, 1-91: e2, 1-91.] Libraries: CU, CtY (1922), ICU, IU, NjP, NNC, RPB, WU A. J. C. CUNNINGHAM; and J. CULLEN. 1. "On idoneal numbers," Br. Ass. Adv. Sci., Report, 1901, p. 552. [f,.] A. J. C. CUNNINGHAM and T. COSSET. 1. "4-tic and 3-bic residuacity tables," Messenger Math., v. 50, p. 1-30 1920. [d6, 26-29.] A. J. C. CUNNINGHAM and H. J. WOODALL. 1. [Solution of problem 14305], Math. Quest. Ed. Times, v. 73, 1900, p. 83-94. [dz, 93-94: e,, 86-92.] 2. "Determination of successive high primes," Br. Ass. Adv. Sci., Report, 1900, p. 646. [fi.] 3. "Determination of successive high primes (second paper)," Br. Ass. Adv. Sci., Report, 1901, p. 553. [fi.] 4. "Determination of successive high primes." Messenger Math., v. 31, p. 165-176, 1902. [ti.] [94]

BIBLIOGRAPHY CUN-DATJ 5. "Determination of successive high primes (second paper)," Messenger Math., v. 34, p. 72-89,1904. ft.] 6. "Determination of successive high primes (third paper)," Messenger Math., v. 34, p. 184-192, 1905. ft.] 7. "Haupt-exponents of 2," Quarterly Jn. Math., v. 37, 1905, p. 122-145, [d,*, 142]; v. 42, 1911, p. 241-250, [d,, 248-249: d6, 250]; v. 44, 1912, p. 41-48, 237-242, [df, 45-47, 240-241: d6, 48, 242]; v. 45, 1914, p. 114- 125, [dt, 120-124: d6, 122-125]. 8. "High trinomial binary factorisations and primes," Messenger Math., v. 37, p. 65-83,1907. [e2, 78-82.] 9. Factorisation of Q= (2" + q) and (q.2v+ 1)," Messenger Math., v. 47,1917, p. 1-38. [d4, 28-34: e2, 35-38.] 10. Factorisation ofyn+l, y = 2,3, 5, 6, 7, 10, 11, 12 up to High Powers («), London, 1925, xx+24p. [e2*.] Libraries: CU, CoU, IU, MoU, RPB A. J. C. CUNNINGHAM, H. J. WOODALL and T. G. CREAK. 1. Haupt Exponents, Residue-indices, Primitive Roots and Standard Congru- ences, London, 1922, viii+136 p. [di, 1-32, 97-136: d2, 33-96: e2, 1-32, 97-136.]* Libraries: CU, ICU, IU, MH, NjP, RPB, WU 2. "On least primitive roots," London Math. So., Proc., s. 2, v. 21, 1922, p. 343-358. [di*, 345, 350-358.] H. B. C. DARLING, see HARDY and RAMANUJAN 1. Z. DASE. [See also JACOBI 4.] 1. Factoren-Tafeln filr alle Zahlen der siebenten Million, oder genauer von 6 000 001 bis 7 002 000, mit den darin vorkommenden Primzahlen, Hamburg, 1862, iv+112 p. [d*.] Libraries: CU, CtY, DLC, MdBJ, MB, MH, NN, NNC, PU, RPB 2. Factoren-Tafeln fur alle Zahlen der achten Million, oder genauer von 7 002 001 bis 8 010 000, mit den darin vorkommenden Primzahlen, Hamburg, 1863, p. ii+113-224. [d*.] . Libraries: CtY, MdBJ, MB, MH, NNC, PU, RPB 3. Factoren-Tafeln fur alle Zahlen der neunten Million, oder genauer von 8 010 001 bis 9 000 000, mit den darin vorkommenden Primzahlen [completed by H. R. Rosenberg], Hamburg, 1865, p. i+225-334. [ei*.] Libraries: CtY, MdBJ, MB, MH, PU, RPB P. H. DAUS. 1. "Normal ternary continued fraction expansions for the cube roots of integers," Am. Jn. Math., v. 44, 1922, p. 279-296. [m, 296.] 2. "Normal ternary continued fraction expansions for cubic irrationalities," Am. Jn. Math., v. 51, 1929, p. 67-98. [m, 91-98: p, 91-98.] 3. "Ternary continued fractions in a cubic field," Tdhoku Math. Jn., v. 41, 1936, p. 337-348. [m, 347-348: p, 347-348.] [95]

DAV-DIC BIBLIOGRAPHY H. T. DAVIS. 1. Tables of the Higher Mathematical Functions, v. 2, Bloomington, 1935, xiii+391 p. [fi, 249-250.] Libraries: CPT, CU, CaM, CaTU, CoU, CtY, DLC, ICU, IEN, IU, InU, laAS, laU, KyU, MCM, MH, MiU, MnU, NhD, NjP, NN, NNC, NcD, OCU, OU, PU, RPB, TxU W. DAVIS. 1. "Les nombres premiers de 100 000 001 a 100 001 699," Jn. d. Math., s. 2, v. 11,1866, p. 188-190. [f,*.] C. F. DEGEN. 1. Canon Pellianus sive Tabula simplicissimam aequationis celebratissimae y = oa:2+l solutionem, pro singulis numeri dati valoribus ab 1 usque ad 1000, in numeris rationalibus iisdemque integris exhibens, Copenhagen, 1817, xxiv+112 p. [jif 3-112: m, 3-106.]* Libraries: CtY, MH, NhD, RPB B. N. DELONE. 1. "Ueber den Algorithmus der Erhohung," Leningradskoe Fiziko-Mate- maticheskoe Obshchestvo, Zhurnal, v. 1, 1926-27, p. 257-266; Russian abstract, p. 267. [1, 266: n, 266.] 2. "Darstellung der Zahlen durch binare kubische Formen," Int. Congress Mathems., Bologna, 1928, Atti, v. 2, Bologna, 1928, p. 9-12. [1,11: n, 11.] B. N. DELONE, I. S. SOMINSKII and K. K. BILEVICH. 1. "Tablitsa chisto veshchestvennykh oblastei 4-go poriadka" [Table of totally real fields of degree 4], Akad. Nauk. S.S.S.R., Leningrad, Bull., s. 7, no. 10, 1935, p. 1267-1297. [p, 1295-1297.] E. DESMAREST. 1. Theorie des Nombres. Traite de I'Analyse Indeterminee du second degre d deux inconnues suivi de I'application de cette analyse d, la recherche des racines primitives avec une table de ces racines pour tous les nombres premiers compris entre 1 et 10 000, Paris, 1852, 308 p. [d^ 298-300: d2*, 308:d6,308.] Libraries: ICJ, ICU, IU, MB, MH, MiU, NNC, RPB L. E. DICKSON. 1. "A new extension of Dirichlet's theorem on prime numbers," Messenger Math., v. 33, p. 155-161, 1904. [f2,158-161.] 2. "Theorems and tables on the sum of the divisors of a number," Quar- terly Jn. Math., v. 44, 1913, p. 264-296. [a, 267-290: bf, 291-296.] 3. "Finiteness of the odd perfect and primitive abundant numbers with n distinct prime factors," Am. Jn. Math., v. 35, 1913, p. 413-422. [a, 420- 422.] 4i. History of the Theory of Numbers, v. 1 (Carnegie Inst. Publ. 256), Wash- ington, 1919, xii+486 p. [a, 45-46.] Libraries: CU, CPT, CaM, CaTU, CoU, CtY, DLC, ICJ, ICU, IEN, IU, InU, laAS, [96]

BIBLIOGRAPHY Die IaU, KyU, MdBJ, MB, MH, MiU, MnU, MoU, NhD, NjP, NN, NNC, NRU, NcD, OCU, OU, PEL, PU, RPB, TxU, WvU, WU 42. Reprint, New York, 1934, xii+486 p. [a, 45-46.] Libraries: CPT, CU, CoU, RPB, WvU 5. "All positive integers are sums of values of a quadratic function of x," Am. Math. So., Bull., v. 33, 1927, p. 713-720. [qs, 718-719.] 6. Studies in the Theory of Numbers, Chicago, 1930, x+230 p. [n*, 150-151, 179-180,181-185.] Libraries: CPT, CU, CaM, CaTU, CtY, DLC, ICJ, ICU, IEN, IU, InU, laAS, IaU, KyU, MH, MiU, MnU, MoU, NjP, NN, NNC, NRU, NcD, OCU, OU, PEL, PU, RPB, TxU, WU 7. Minimum Decompositions into Fifth Powers, London, 1933. (Br. Ass. Mathematical Tables, v. 3), vi+368 p. [qs.] Libraries: CU, IU, NhD, NNC, PEL, RPB 8. Researches on Waring's Problem (Carnegie Inst. Publ. 464), Washington, 1935,v+257p.[q3.] Libraries: CU, CPT, CaM, CaTU, CoU, CtY, DLC, ICJ, ICU, IEN, IU, InU, laAS, IaU, KyU, MdBJ, MB, MH, MiU, MnU, MoU, NhD, NjP, NN, NNC, NRU, NcD, OCU, OU, PEL, RPB, TxU, WvU, WU 9. Modern Elementary Theory of Numbers, Chicago, 1939, viii+309 p. [n, 58,79,112-113.] Libraries: CPT, CU, CaM, CtY, DLC, ICJ, ICU, laAS, IaU, InU, MB, MH, MiU, MnU, MoU, NhD, NjP, NN, NNC, NRU, NcD, OU, RPB, WU 10. Table of the unique solution x of l+gn = g* (mod p) for a given «, and a given primitive root g of the prime p, Manuscript, [k.] Libraries: ICU 11. Table of minimum decompositions into fifth powers of the integers from 839 000 to 929 000, 1 466 800 to 1 600 000, Manuscript, [q,.] Libraries: ICU 12. Table of minimum number of cubes required to represent each integer from 40 000 to 270 000, Manuscript. [qa.] Libraries: ICU 13. Table of sums of four cubes from 270 000 to 560 000, Manuscript. [q».] Libraries: ICU 14. History of the Theory of Numbers (Carnegie Inst. Publ. 256), Wash- ington, v. 1, 1919; v. 2, 1923; v. 3, 1927. Reprint, 3 v., New York, 1934. In these volumes are references to tables supplementary to those men- tioned in the report. A list of such references, arranged according to classifications of this report, follows (see Introduction): a v. 1 ch. I, no. 42. e, v. 1, ch. XIII. ch. V, no. 94. e. v. 1, ch. I, nos. 89, 139: ch. VI, nos. 14, ch. I, no. 363. 26,35,37, 50, 109, 141: ch. XVI: ch. ch. IV, no. 29. XX, no. 27. ch. VI, nos. 8, 9. fi v. 1, ch. VI, no. 13: ch. XIII. bi v. 1 bi v. 1 b4 v. 1 c v. 1 di v. 1, ch. VII, nos. 2, 4, 55. f. v. 3, ch. I, no. 16. d, v. 1, ch. VI, nos. 8, 9. g v. 1, ch. XIV, no. 37. di v. 1, ch. VH, nos. 54,105: ch. VIII, nos. h v. 2, ch. II, no. 41. 80, 94. i, v. 3, ch. I, no. 20. d4 v. 1, ch. I, no. 54: ch. Ill, no. 235. j, v. 2, ch. XII, nos. 65, 72, 82, 99, 102, [97]

DIN-EUL BIBLIOGRAPHY 107, 135, 273. 1 v. 2, ch. XX, nos. 56, 58: ch. XXII, j» v. 2, ch. XVI, nos. 1, 70, 77: v. 3, ch. no. 107. I, nos. 16, 94. m v. 2, ch. XII, nos. 145, 232, 273. j, v. 2, ch. IV, nos. 42, 96, p. 189-190: n v. 3, ch. I, nos. 18, 126: ch. II, no. 31: ch. V, nos. 16, 31, 48, 59: ch. VIII, ch. IV, nos. 14, 15: ch. V, no. 196 no. 41. (p. 150): ch. IX, no. 20. k v. 1, ch. Vin, nos. 136, 137. q, v. 2, ch. Ill, nos. 9, 32, 77. Libraries: See 4i above. L. L. DINES. 1. "A method for investigating numbers of the form 6*J+1," Annals of Math., s. 2, v. 10,1909, p. 105-115. [f2*, 111-115.] W. P. DURFEE. 1. Factor table for the 16th million, Manuscript, compiled 1923-29. For a complete account of the table see Scripta Math., v. 4, 1936, p. 101. [d*: t.] Libraries: Am. Math. So., New York City. W. C. EELLS. 1. [Solution of a problem], Am. Math. Mo.,\. 21, 1914, p. 271-273. [J3.] G. ElSENSTEIN. 1i. "Neue Theoreme der hoheren Arithmetik," Jn. f. d. reine u. angew. Math., v. 35, 1847, p. 117-136. [n, 136.] 12. Mathematische Abhandlungen, Berlin, 1847, p. 177-196. [n, 196.] Libraries: CPT, CU, CaM, CoU, CtY, ICU, IEN, IU, MB, MH, NhD, NjP, NNC, NcD, OCU, RPB, WU 2. "Tabelle der reducirten positiven ternaren quadratischen Formen, nebst den Resultaten neuer Forschungen iiber diese Formen, in besonderer Riicksicht auf ihre tabellarische Berechnung," Jn. f. d. reine u. angew. Math., v. 41, 1851, p. 141-190. [n, 169-190.] 3. " Anhang zu der 'Tabelle der reducirten positiven ternaren quadratischen Formen, etc.' im vorigen Hefte," Jn. f. d. reine u. angew. Math., v. 41, 1851, p. 227-242. [n.] ]. D. ELDER, see D. N. LEHMER 32. E. B. ESCOTT. [See also POULET 5.] 1i. "The converse of Fermat's theorem," Messenger Math., v. 36, p. 175— 176, 1907. [d,, 176.] 12. French transl. by J. FITZ-PATRICK, "L'lnverse du th6oreme de Fermat," Sphinx Oedipe, v. 2, 1907, p. 146-148. [d,, 147-148.] L. EULER. 1i. "De numeris amicabilibus," Opuscula Varii Argumenti, Berlin, v. 2, 1750, p. 23-107. [a, 105-107: b2, 27-32: e2, 27-32.] Libraries: DLC, ICJ, ICU, IU, MdBJ, MH, NjP, NN, RPB 12. Commentationes Arithmeticae, St. Petersburg, v. 1, 1849, p. 102-145. [a, 144-145: t>2, 104-109: e2, 104-109.] [98]

BIBLIOGRAPHY FAD-GAU Libraries: CU, ICU, KyU, MdBJ, MH, NN, NNC, RPB 13. Opera Omnia, Leipzig, s. 1, v. 2,1915, p. 86-162. [a, 159-162: b2, 90-95: e,, 90-95.] Libraries (also for s. 1, v. 3): CU, CaM, CtY, DLC, ICJ, ICU, IEN, IU, laAS, laU, MdBJ, MH, MiU, MnU, NhD, NjP, NN, NNC, NcD, OCU, PU, RPB, TxU, VVU 14. French transl. in Sphinx Oedipe, v. 1, 1906, Supplement, p. i-lxxvi. [a, Ixxv-lxxvi: b2, iv-xi: e2, iv-xi.]* 1i. "De numeris primis valde magnis," Acad. Sci. Petrop., Novi Commen- tarii, v. 9 (1762-3), 1764, p. 99-153. [e2, 128-153: f2, 123-127:1i, 112-117.] 22. Commentationes Arithmeticae, v. 1, 1849, p. 356-378. [e2, 369-378: fs, 367-369: h, 362-364.] 2a. Opera Omnia, s. 1, v. 3,1917, p. 1-45. [e2, 26-45: f2, 22-25: ii, 13-17.] 24. French transl. in Sphinx Oedipe, v. 8, 1913, p. 1-12, 21-26. [e», 11-12, 21-26: f2, 10-11: h, 7.] 3i. "De partitione numerorum," Acad. Sci. Petrop., Novi Commentarii, v. 3 (1750-1), 1753, p. 125-169. [q,, 165-169.] 32. Commentationes Arithmeticae, v. 1, 1849, p. 73-101. [qi, 97-101.] 33. Opera Omnia, s. 1, v. 2, 1915, p. 254-294. [qi, 290-294.] D. K. FADDEEV. 1. "Ob uravnenii [on the equation] x*+y* = Az3," Akad. Nauk S.S.S.R., Leningrad, Fiz-mat. Inst. imeni V. A. Stekloff, Trudy, v. 5,1934, p. 25- 40. [1,40.] A. FLECHSENHAAR. 1. "Die Gleichung x"+y"-zn = 0 (mod «2)," Z. f. math. u. natw. Unter- richt, v. 40, 1909, p. 265-275. [k, 275.] M. FROLOV. 1. "Sur les residus quadratiques," Ass. Franc, pour 1'Avan. d. Sci., Comptes Rendus, v. 21, pt. 2, 1892, p. 149-153. [i2, 158-159.] E. R. GARBE. 1. New Waring theorems for extended polygonal numbers (Master's the- sis, Chicago), Chicago, 1937, i+13 p. Manuscript. [q3.] Libraries: ICU K. F. GAUSS. li. Disquisitiones Arithmeticae, Leipzig, 1801, xviii+668+app. 10 p. [c, 5- 6:d3, 1-2: i2, 3-4: o,638,665.] Libraries: CtY, DLC, IEN, IU, laU, MB, MH, MiU, NN, NNC, PU, RPB, TxU 12. Werke, v. 1, Gottingen, 1863, second ed.,i 1870, 474 p. [c, 470: ds, 468: it, 469: o, 357, 463.] Libraries: I ed. CU, CaM, CtY, ICJ, ICU, NN, RPB; II cd. CPT, CaM, CaTU, CtY, i In all double entries under Gauss, we have not given separate numbers to articles in the first and second editions of Gauss' Werke, v. 1-2, where the page numbers are identical in GAUSS 1-7. [99]

GER BIBLIOGRAPHY DLC, IEN, laAS, laU, IU, KyU, MdBJ, MB, MH, MiU, NhD, NjP, NNC, NcD, OCU, OU, PU, RPB, TxU, WU I3. Recherches Arithmetiques, French transl. by A. C. M. POULLET-DELISLE, Paris, 1807, xxii+502 p. [c, 501-502: d3, 497-498: i2, 499-500: o, 469, 489.] Libraries: CaTU, CtY, DLC, ICJ (1910), ICU, InU, MB, MH, MiU, NhD, NNC, NcD (1910), PU, RPB 14. Untersuchungen iiber hohere Arithmetik, German transl. by H. MASER of the Disquisitiones (p. 1-448, 451-453), with "Zusatze" (p. 449-450) and "Abhandlungen" and Gauss "Nachlasse" with "Bemerkungen" (p. 455-695), Berlin, 1889, xiii+695 p. [c, 453: d3, 451: i2, 452: o, 428, 448.] Libraries: CU, ICU, IU, MH, MiU, MnU, NNC, PU, RPB, TxU 2i. "Theoria residuorum biquadraticorum," Gesell. d. Wiss. z. Gottingen, Commentationes . . . recentiores, Cl. math., v. 6, 1828, p. 27-56; v. 7, 1832, p. 89-148. [dB, 35-37: p, 131-133.] 2|. Werke, v. 2,1863, second ed., 1876, p. 65-92, 93-148. [d6, 73-75: p, 132- 134.] Libraries: I ed. CU, CaM, CtY, ICJ, ICU, NN, NNC, RPB; II ed. CPT, CaM, CaTU, CtY, DLC, IU, InU, laAS, laU, KyU, MdBJ, MB, MH, MiU, NhD, NjP, NNC, NcD, OCU, OU, PU, RPB, TxU, WU 3. "De nexu inter multitudinem classium, in quas formae binariae secundi gradus distribuuntur, earumque determinantem," Werke, v. 2,1863, sec- ond ed., 1876, p. 269-291. [i,, 287-291: qi, 271.] 4. "Tafel des quadratischen Characters der Primzahlen von 2 bis 997 als Reste in bezug auf die Primzahlen von 3 bis 503 als Theiler," Werke, v. 2, 1863, second ed., 1876, p. 400-409. [i,.] 5. "Tafel zur Verwandlung gemeiner Briiche mit Nennern aus dem ersten Tausend in Decimalbruche," Werke, v. 2, 1863, second ed., 1876, p. 412-434. [c.] 6. "Tafel der Frequenz der Primzahlen," Werke, v. 2, 1863, second ed., 1876, p. 436-443. [if.] 7. "Tafel der Anzahl der Classen binarer quadratischer Formen," Werke, v. 2,1863, second ed., 1876, p. 450-476. [n*.] 8. "Tafel zur Cyklotechnie," Werke, v. 2, 1863, p. 478-495, second ed., 1876, p. 478-496. [e2.] 9. "Indices der Primzahlen im hohern Zahlenreiche," Werke, v. 2,1876, p. 506. [Not in first ed.] [p.] 10. "Hiilfstafel bei Auflosung der unbestimmten Gleichung A =fxx-\-gyy vermittelst der Ausschliessungsmethode," Werke, v. 2,1876, p. 507-509. [Not in first ed.] [ii.] A. GERARDIN. 1. "Table des nombres dont 10 est racine primitive et nombres de la forme 10"-1," Sphinx Oedipe, v. 3, p. 101-112, 1908. [d2, 107-110: dt, 107- 110:e2, 104-106.] 2. "Table des residus quadratiques," Sphinx Oedipe, v. 9, p. 21-22, 1914. [ii:i,.] 3. "Congruences 2y4-1 =0 (mod p), Sphinx Oedipe, v. 9, p. 20, 1914. [d4.] [100]

BIBLIOGRAPHY GIF-GLA 4. "Au sujet d'un probleme de Fermat," L'Intermediaire d. Math., v. 22, 1915, p. 111-114. [e2, 112-113.] 5. "Sur 1'equation x3±y*= ±a," Sphinx Oedipe, v. 10, p. 53-57, 65-70, 83-88, 1915; v. 11, p. 4-8, 22-27, 38-43, 55-59, 71-76, 86-88, 1916; v. 12, p. 8-12, 21-24, 38-40, 54-56, 71-74, 1917. [1.] 6. "Factorisations quadratiques et primalite, 1," Sphinx Oedipe, v. 27, 1932, 96+app. 7 p. [ft, app.] 7. Table of the Pell Equation. Manuscript in the possession of the author, [ji-] E. GIFFORD. [See also PETERS, LODGE and TERNOUTH, GIFFORD.] 1. Primes and Factors, Manchester, 1931, v+99 p. [ei*.] Libraries: CU, DLC, NhD, NN, RPB D. GlGLI. 1. "Sulle somme di » addendi diversi presi fra i numeri 1, 2, • • • , m," Circolo Mat. d. Palermo, Rendiconti, v. 16, 1902, p. 280-285. [qi, 284.] J. GLAISHER. 1. Factor Table for the Fourth Million, Containing the Least Factor of Every Number Not Divisible by 2, 3, or 5 between 3 000 000 and 4 000 000, London, 1879. 52 + 112 p. [e,*, 1-112: f,, 40-45, 48-52.] Libraries: CU, CtY, DLC, ICU, IU, MdBJ, MB, MH, NhD, NN, NNC, PU, RPB 2. Factor Table for the Fifth Million, Containing the Least Factor of Every Number Not Divisible by 2, 3, or 5 between 4 000 000 and 5 000 000, London, 1880,11 + 112 p. [ei*, 1-112: f,, 6-10.] Libraries: CU, CtY, DLC, ICU, IU, MB, MH, NN, NNC, PU, RPB 3. Factor Table for the Sixth Million, Containing the Least Factor of Every Number Not Divisible by 2, 3, or 5 between 5 000 000 and 6 000 000, London, 1883, 103 + 112 p. fd*, 1-112: fi, 10-64, 71-76, 80-88.] Libraries: CU, CtY, DLC, ICU, IU, MB, MH, NhD, NN, NNC, PU, RPB J. W. L. GLAISHER. 1. "On the law of distribution of prime numbers," Br. Ass. Adv. Sci., Re- port, 1872, Sectional Trans., p. 19-21. [fi.] 2. "Preliminary account of the results of an enumeration of the primes in Base's tables (6,000,000 to 9,000,000)," Cambridge Phil. So., Proc., v. 3, p. 17-23,1876. [fi, 21-23.] 3. "Preliminary account of an enumeration of the primes in Burckhardt's tables (1 to 3,000,000)," Cambridge Phil. So., Proc., v. 3, p. 47-56,1877. [fi, 54-56.] 4. "On circulating decimals," Cambridge Phil. So., Proc., v. 3, p. 185-206, 1877. [bi, 204-206: c, 204-206: d2, 204-206.] 5. "On the value of the constant in Legendre's formula for the number of primes inferior to a given number," Cambridge Phil. So., Proc., v. 3, p. 296-309, 1877. [f,.] 6. "On the enumeration of the primes in Burckhardt's and Base's tables," Br. Ass. Adv. Sci., Report, 1877, Sectional Trans., p. 20-23. [fi.] [101]

GLA BIBLIOGRAPHY 7. "On long successions of composite numbers," Messenger Math., v. 7, p. 102-106, 171-176, 1877-8. [f,, 104, 105, 171-176.] 8. "An enumeration of prime-pairs," Messenger Math., v. 8, 28-33, 1878. [fi-1 9. "On certain special enumerations of primes," Br. Ass. Adv. Sci., Report, 1878,p. 470-471. [fi:f2.]* 10. "Note on the enumeration of primes of the forms 4« + l and 4«+3," Br. Ass. Adv. Sci., Report, 1879, p. 268. [f2.] 11. "Report of the committee ... on mathematical tables," Br. Ass. Adv. Sci., Report, 1879, p. 46-57. [fi, 47-49.] 12. "Separate enumerations of primes of the form 4«+l and of the form 4«+3," Royal So. London, Proc., v. 29, 1879, p. 192-197. [f2, 195-197.] 13. "Report of the committee ... on mathematical tables," Br. Ass. Adv. Sci., Report, 1880, p. 30-38. [fi.] 14. "Report of the committee ... on mathematical tables," Br. Ass. Adv. Sci., Report, 1881, p. 303-308. [fi.] 15. "On the function which denotes the difference between the number of (4m+l)-divisors and the number of (4m+3)-divisors of a number," London Math. So., Proc., s. 1, v. 15, p. 104-122, 1884. [b2, 106: n, 106.]* 16. "Report of the committee ... on mathematical tables," Br. Ass. Adv. Sci., Report, 1883, p. 118-127. [fi.] 17. "On the representations of a number as the sum of four uneven squares, and as the sum of two even and two uneven squares," Quarterly Jn. Math., v. 20, 1885, p. 80-167. [b2, 164-165: f2, 151-154: n, 164-165: p, 151-154.] 18. "On the square of Euler's series," London Math. So., Proc., s. 1, v. 21, p. 182-215, 1889. [b2, 190-192: n, 190.] 19. "On the function which denotes the excess of the number of divisors of a number which =1, mod 3, over the number which =2, mod 3," London Math. So., Proc., s. 1, v. 21, p. 395-402, 1890. [b2, 402: n, 402.] 20. "On the sums of the inverse powers of the prime numbers," Quarterly Jn. Math., v. 25,1891, p. 347-362. [fi, 353.] 21. "On the series l/32-1/52+l/72+l/ll2-l/132- • • • ," Quarterly Jn. Math., v. 26, 1893, p. 33-47. [e2, 47.] 22. "Table of the values of i -f • j • • • (x— l)/x, the denominators being the series of prime numbers," Messenger Math., v. 28, p. 2-15, 1898. [fi.] 23. "Congruences relating to the sums of products of the first n numbers and to other sums of products," Quarterly Jn. Math., v. 31, 1900, p. 1- 35. [b6, 26-28.] 24. "Table of the excess of the number of (3^ + 1)-divisors of a number over the number of (3£ + 2)-divisors," Messenger Math., v. 31, p. 64-72,1901. [b2, 67-72 :n, 67-72.] 25. "Table of the excess of the number of (8£+l)- and (8£+3)-divisors of a number over the number of (8A+5)- and (8£ + 7)-divisors," Messenger Math., v. 31, p. 82-91, 1901. [b2, 86-91: n, 86-91.] 26. "On some asymptotic formulae relating to the divisors of numbers," Quarterly Jn. Math., v. 33, 1902, p. 1-75,180-229. [b2,42,193, 204, 213.] [102]

BIBLIOGRAPHY GOL-GRA 27. Number-Divisor Tables (Br. Ass. Mathematical Tables, v. 8), Cambridge 1940, x+100 p. [bi, 2-71: bt, 2-63, 72-100: d, 2-63.] B. GOLDBERG. 1. Primzahlen- und Factoren-Tafeln von 1 bis 251 647, Leipzig, 1862, 285 P- [6i*.] Libraries: RPB 2. Rest- und Quotient-Rechnung, Hamburg, 1869,138 p. [di, 97-138.] Libraries: NNC V. GOLUBEV. 1. Factor table of the eleventh and twelfth millions. Manuscript, [d.] Libraries: Stekloff Inst., Moscow. H. GOODWYN. 1. The First Centenary of a Series of Concise and Useful Tables of All the Complete Decimal Quotients which can arise from dividing a unit, or any whole number less than each divisor, by all integers from 1 to 1024. To which is now added a tabular series of complete decimal quotients for all the proper vulgar fractions of which, when in their lowest terms, neither the numerator nor the denominator is greater than 100; with the equivalent vulgar fractions prefixed, London, 1818, xiv + 18; vii+30 p. [bi: C.] Libraries: CtY (specimen 1816), RPB 2. A Tabular Series of Decimal Quotients for All Proper Vulgar Fractions of which, when in their lowest terms, neither the numerator nor the denomi- nator is greater than 1000, London, 1823, v+153 p. [bi: C.] Libraries: ICJ 3. A Table of Circles arising from the Division of a Unit, or Any Other Whole Number, by All the Integers from 1 to 1024, being all the pure decimal quotients that can arise from this source, London, 1823, v+118 p. [c.] Libraries: T. COSSET. [See also CUNNINGHAM and COSSET.] 1. "On the law of quartic reciprocity," Messenger Math., v. 41, p. 65-90, 1911. [d,, 84-85.] C. GOUWENS. 1. "The decomposition of 4(x"- !)/(*-1)," Am. Math. Mo., v. 43, 1936, p. 283-284. [o*.] 2. "The decomposition of 4(x"- !)/(*-1)," Iowa Acad. Sci., Proc., v. 43, 1936, p. 225-262; v. 44, 1937, p. 137-138. [o.] J. P. GRAM. 1. "Unders^gelser angaaende msengden af primtal under en given graense," K. Danske Vidensk. Selskabs, Skrifter, s. 6, v. 2, p. 183-288, 1884. [b3, 268-286 :f,, 268-288.] 2. "Rapport sur quelques calculs enterpris par M. Bertelsen et concernant les nombres premiers," Acta Math., v. 17,1893, p. 301-314. [fi, 312-314.] [103]

GRA-HAR BIBLIOGRAPHY D. O. GRAVE. 1. "Pro prosti Cislavjdu p = 4n-\-3," [On the primes of the form 4«+3], Vseukrajins'ka Akad. Nauk, Kief, Zurnal mat. ciklu (anno 3), v. 1, no. 4, 1934, p. 91-95. [o*, 93-95.] 2. "Pro dejaki kvadraticni polja," [On certain quadratic fields], Vseu- krajins'ka Akad. Nauk, Kief, Zurnal mat. ciklu (anno 3), v. 1, no. 4, 1934, p. 97-112. [o*, 98-109.] 3. Traktat 2 Algebrichnogo Analizu, v. 2, Kiev, 1938, 400 p. [di*, 362-391: d3, 362-391: e,*, 325: q2*, 19-22.] Libraries: CU, CtY, DLC, NN, NNC, RPB H. GUPTA. 1. "A table of partitions," London Math. So., Proc., s. 2, v. 39, 1935, p. 142-149; v. 42, 1937, p. 546-549. [qi.] 2. "Decompositions into squares of primes," Indian Acad. Sci., Proc., sect. A, v. 1, 1935, p. 789-794. [q3, 790-794.] 3. "On a conjecture of Ramanujan," Indian Acad. Sci., Proc., sect. A, v. 4, 1936, p. 625-629. [qi, 626-629.] 4. "Decompositions into cubes of primes II," Indian Acad. Sci., Proc., sect. A, v. 4, 1936, p. 216-221. [q3, 217-220.] 5. "Decompositions into cubes of primes," Tdhoku Math. Jn., v. 43, 1937, p. 11-16. [qs, 12.] 6. "On a conjecture of Chowla," Indian Acad. Sci., Proc., sect. A, v. 5, 1937, p. 381-384. [qs, 382-384.] 7. Tables of Partitions, Madras, The Indian Mathematical So., 1939, vi+82 p. [q,, 8-81.] Libraries: IU, RPB M. HABERZETLE. 1. Representation of large integers by cubic polynomials (Master's thesis, Chicago), Chicago, 1936, iii+27 p. Manuscript. [qs.] Libraries: ICU E. H. HADLOCK. 1. "Progressions associated with a ternary quadratic form," Am. Jn. Math., v. 57, 1935, p. 274-275. [n.] M. HALL. 1. "Slowly increasing arithmetic series," London Math. So., Jn., v. 8,1933, p. 162-166. [b«, 166: C2, 166.] G. B. HALSTED. 1. Metrical Geometry, and Elementary Treatise on Mensuration, Boston, 1881, vii+232 p. [j3*, 147-149, 167-170.] Libraries: CPT, CU, IEN, IU (1900), InU (1883), laAS, MiU, MnU, NjP, NNC (1900), NcD, RPB G. H. HARDY and J. E. LITTLEWOOD. 1. "Partitio numerorum III: On the expression of a number as a sum of [104]

BIBLIOGRAPHY HAR-HOU primes," Acta Math., v. 44, 1923, p. 1-70. [fi, 39, 43, 44, 63: q2, 39.] 2. "Some problems of partitio numerorum VIII," London Math. So., Proc., s. 2, v. 28, 1928, p. 518-542. [q3, 540-542.] G. H. HARDY and S. RAMANUJAN. li. "Asymptotic formulae in combinatory analysis," London Math. So., Proc., s. 2, v. 17, 1918, p. 75-115. [qi*, 112-115.] Is. Collected Papers of Srinivasa Ramanujan, Cambridge, 1927, p. 276-309. [qi*, 306-309.] Libraries: CPT, CU, CaM, CoU, CtY, DLC, ICU, IU, laAS, laU, MdBJ, MCM, MH, MiU, NhD, NjP, NN, NcD, OCU, OU, PU, RPB, WU R. HAUSSNER. 1. "Tafeln f iir das Goldbachsche Gesetz," K. Leop. Carol Deutschen Akad. d. Naturforscher, Abhandlungen, v. 72, no. 1, Halle, 1897. [q2*, 25-178, 181-191,195-210.] 2. "Reste von 2V~i— 1 nach dem Teiler />2 fur alle Primzahlen bis 10 009," Archivfor Math, og Naturvidenskab, v. 39, no. 2, 17 p., 1925-6. [b4, 6-17: ds, 6-17.] 3. "tlber numerische Losungen der Kongruenze u"~i—l=0 (mod />2)," Jn.f. d. reine u. angew. Math., v. 156, 1926, p. 223-226. [b4, 226.] 4. "Untersuchungen iiber Liickenzahlen und den Goldbachschen Satz," Jn.f. d. reine u. angew. Math., v. 158, 1927, p. 173-194. [q,, 193-194.] M. A. HEASLET, see USPENSKY and HEASLET. H. HERTZER. 1. "Periode des Dezimalbruches flir l/p, wo p eine Primzahl," Archiv Math. Pkys., s. 3, v. 2, 1902, p. 249-252. [d,*.] H. HOLDEN. 1. "On various expressions for h, the number of properly primitive classes for a determinant — p, where p is a prime of the form 4«+3," Messenger Math., v. 35, p. 73-80, 1905. [o, 79-80.] 2. "On a property of the function Z in the transformation 4XP=Y* -(-l)<"-i>/*/>Zy Messenger Math., v. 37, p. 130-139, 1908. [o, 136- 137.] S. HOPPENOT. [See also KRAITCHIK and HOPPENOT.] 1. "Courrier du Sphinx," Sphinx, Brussels, v. 4, 1934, p. 189-190; v. 5, 1935, p. 48. [e,.] 2. Tables des Solutions de la Congruence **= -1 (mod N) pour 100 000 < N <200 000, (Librairie du Sphinx), Brussels, 1935, 18 p. [d4.] Libraries: RPB J. HOUEL. [See also LEBESGUE 2.] 1. Tables Arithmetiques, Paris, 1866, 44 p. [c, 41-44: d3, 30-40.] Libraries: CU, MH, RPB [105]

HUS-JAC BIBLIOGRAPHY M. HUSQUIN. 1. "Etude statistique des nombres premiers," Sphinx, Brussels, v. 4, 1934, p. 147. [f,.] E. L. INCE. 1. Cycles of Reduced Ideals in Quadratic Fields. (Br. Ass. Mathematical Tables, v. 4) London, 1934, xvi+80 p. [jt: m: p.] Libraries: CoU, CtY, IU, NNC, RPB G. INGHIRAMI. It. Elementi di Matematiche, Florence, v. 1, 1832. [Ct.] Libraries: Is. Cor so Elementare di Matematiche Pure, riordinate per cura di G. Antonelli ed. E. Barsanti, Florence, v. 1, 1856. [ei.] Libraries: la. Table des Nombres Premiers et de la Decomposition des Nombres de 1 a 100 000 . . . suiviedela Table des Bases des Nombres Tessareens de 1 a 20 000, Paris, 1919, xi+35 p. [e,*.] Libraries: NjP, NN, NNC, RPB K. G. J. JACOBI. It. "Beantwortung der Aufgabe s. 212 dieses Bandes." Jn. f. d. reine u. angew. Math., v. 3, p. 301-302, 1828. [d4.] l2. Gesammelte Werke, Berlin, v. 6, 1891, p. 238-239. [d4.] Libraries: CU, CaM, CaTU, CoU, CtY, DLC, ICJ, ICU, IU, laAS, laU, KyU, MdBJ, MB, MCM, MH, MiU, MnU, NhD, NjP, NNC, NcD, OCU, OU, PEL, PU, RPB, TxU, WU 2. Canon Arithmeticus, sive tabulae quibus exhibentur pro singulis numeris primis vel primorum potestatibus infra 1000 numeri ad datos indices et indices ad datos numeros pertinentes, Berlin, 1839, xl+248 p. [di, 1-248: d2, iii-v:d,, 1-248.]* Libraries: CPT, DLC, laAS, MH, MiU, MnU, NhD, NN, PU, RPB 3i. "Uber die Kreistheilung und ihre Anwendung auf die Zahlentheorie," Jn.f. d. reine u. angew. Math., v. 30, p. 166-182, 1846. [J2*, 174-180: k, 181-182.] 32. Opuscula Math., Berlin, v. 1, 1846, p. 317-334. [j2*, 326-332: k, 333- 334.] Libraries: laAS, MH, MiU, NhD, PU, RPB 3,. Gesammelte Werke, Berlin, v. 6, 1891, p. 254-274. [j,*, 265-271: k, 272- 274.] 4i. "liber die Zusammensetzung der Zahlen aus ganzen positiven Cuben; nebst einer Tabelle f iir die kleinste Cubenanzahl, aus welchen jede Zahl bis 12 000 zusammengesetzt werden kann," Jn. f. d. reine u. angew. Math., v. 42, p. 41-69, 1851. [q,, 62-69.] 42. Opuscula Math., v. 2, 1851, p. 361-389. [q3, 382-389.] 48. Gesammelte Werke, v. 6, 1891, p. 322-354. [q3, 346-354.] [106]

BIBLIOGRAPHY JOF-KOR S. A. JOFFE. 1. Solutions of *2+y2+z2 = w2. Manuscript in possession of the author. Libraries: RPB (copy) E. DE JONCOURT. 1. De Natura et Praeclaro usu Simplicissimae Speciei Numerorum Tri- gonalium, The Hague, 1762, viii+36+224+7 p. [b7,1-224.] Libraries: NN, RPB B. W. JONES. 1. A Table of Eisenstein-reduced Positive Ternary-Quadratic Forms of De- terminant ^200 (Nat. Research Council, Bull. no. 97), Washington, Nat. Acad. Sci., 1935, 51 p. [n.] Libraries: CU, CaTU, CtY, DLC, ICJ, IEN, IU, laAS, MdBJ, MB, MCM, MH, MiU, MnU, NjP, NN, OCU, OU, PEL, RPB B.W. JONES and G. PALL 1. "Regular and semi-regular positive, ternary quadratic forms," Acta Math., v. 70, 1939, p. 165-191. [n, 190-191.] C. F. KAUSLER. 1. "De Numeris qui semel vel pluries in summam duorum quadratorum resolvi possunt," Akad. Nauk, S.S.S.R., Leningrad, Nova Acta, v. 14, ad annos 1797-8, p. 232-267, 1805. [b7, 253-267.] J. KAVAN. li. Rozklad Vsetkych Cisel Celych od 2 do 256 000 v Prvocinitele and on the second title-page: Tabula Omnibus a 2 usque ad 256 000 Numeris Integris Omnes Divisores Primos Praebens (Observatorium Publicum, Stara Dala, Bohemoslov), Prague, 1934, xi+514 p. [ft.] Libraries: CU, CaM, ICU, NjP, NNC, RPB 12. Factor Tables giving the Complete Decomposition into Prime Factors of All Numbers up to 256 000 • • • . With prefaces by B. Sternbeck and K. Petr, and introduction by Arthur Beer. London, 1937, xii+514 p. [fi.l Libraries: MiU, NN, NNC, RPB F. KESSLER, see BORK. C. Ko. 1. "Decompositions into four cubes," London Math. So., /n., v. 11, 1936, p. 218-219. [q,, 219.] A. N. KORKIN. 1. "O raspredelenii tselykh chisel po prostomu moduliu i o dvuchlennykh sravneniakh s tablitsefu pervoobraznykh kernel i kharakterov k nim otnosiashchikhsia, dlia prostykh chisel men'shikh 4000" [On the distribu- tion of integers with respect to a prime modulus and on binomial con- gruences with a table of primitive roots and of characters corresponding [107]

KRA-KRI BIBLIOGRAPHY to them for all primes less than 4000], Matematicheskil Sbornik, v. 27, 1909, p. 28-115, 121-137. [di, 121-137: d,, 121-137: e,, 121-137.] M. KRAITCHIK. 1. "Tables," Sphinx Oedipe, May 1911, Numero Special, p. 1-10; v. 6, 1912, p. 25-29, 39-42, 52-55. [di: d,.] 2. Decomposition de a" + bn en Facteurs dans le Cas oil nab est un Carrt Parfait avec une Table des Decompositions Numfriques pour Toutes Its Valeurs deaetb Inferieurs A 100, Paris, 1922, 16 p. [e,, 9-16: o*, 3, 6.] Libraries: CU, CtY, IU, laAS, NjP, NcD, PJJ, RPB 3. Theorie des Nombres, v. 1, Paris, 1922, ix+229 p. [d3*, 214-217: d(, 208- 213: e2, 218-222: if, 187-204: it, 205-207: i3*, 164-186.] Libraries: CU, CaM, CoU, CtY, ICU, IU, laAS, MdBJ, MCM, MH, MnU, MoU, NjP, NN, NNC, OCU, OU, PEL, PU, RPB, WU 4. Recherches sur la Theorie des Nombres, v. 1, Paris, 1924, xvi+272 p. [bi, 23: di*, 55-58, 61, 131-145: Af, 53, 55, 63-65, 131-204: d3*, 69-70, 216-267: d4, 62-63: d6*, 39-41, 59-63: e2*, 12-14, 20, 24-26, 77-80, 92: fi*, 10, 14-16, 131-191: if, 9-12, 15-16, 53, 192-204: h, 27, 69: i,, 46, 87: i2, 46: i3*, 205-215: if, 46, 48-50: J2*, 48-50, 192-204: k, 39-41: o*, 88, 93-129, 270.] Libraries: CU, CoU, CtY, ICU, IU, InU, laAS, MH, MiU, NjP, NN, NNC, OCU, PEL, PU, RPB, WU 5. "Sur les nombres de Fermat," Inst. d. France, Acad. d. Sci., Comptes Rendus, v. 180, 1925, p. 799-801. [e,.] 6. Theorie des Nombres, v. 2, Paris, 1926, iv+251 p. [d2*, 233-235: e2*, 221- 232: f2, 233-235: if, 156-166: J3*, 241-242: m*, 30-71: n, 119.] Libraries: CU, CaM, CoU, ICU, IU, InU, laAS, MdBJ, MCM, MH, MiU, MnU, MoU, NjP, NNC, NcD, OCU, OU, PEL, PU, RPB, WU 7. Recherches sur la Theorie des Nombres, v. 2, Paris, 1929, xv+184 p. [b2, 152-159: e2, 84-150, 152-159: o, 2-4, 6.]* Libraries: CtY, InU, laU, MiU, NjP, NN, PU, RPB 8. "Factorisation de 24a+l," Sphinx, Brussels, v. 2, 1932, p. 84-85. [e2.] 9. "Les grands nombres premiers," Mathematica, Cluj, v. 7,1933, p. 92-94. [if, 93.] 10. "Sur les nombres premiers," Sphinx, Brussels, v. 3, 1933, p. 100-101. [f..] 11. "Courrier du Sphinx," Sphinx, Brussels, v. 4, 1934, p. 48. [e2.] 12. "Les grands nombres premiers," Deuxieme Congres Int. d. Recreation Math., Comptes Rendus, Brussels, 1937, p. 69-73. [d: £t.] 13. "Factorisation de 2"± 1," Sphinx, Brussels, v. 8, 1938, p. 148-150. [e2.] M. KRAITCHIK and S. HOPPENOT. 1. "Les grands nombres premiers," Sphinx, Brussels, v. 6, 1936, p. 162- 166; v. 8, 1938, p. 82-86. [d: f,.] A. A. KRISHNASWAMI. 1. "On isoperimetrical pythagorean triangles," Tohoku Math. Jn., v.27, 1927, p. 332-348. [J3, 344-347.] [108]

BIBLIOGRAPHY KUL-LEB J. P. KULIK. 1. Tafeln der Quadrat- und Kubik-Zahlen aller natiirlichen Zahlen bis Hundert Tausend, nebst ihrer Anwendung auf die Zerlegung grosser Zahlen in ihre Faktoren, Leipzig, 1848, vii+460 p. [f2, 405-407: g, 408- 418: ii, 408-418: J2, 405-407:1, 407-408.] Libraries: MH, NNC, RPB 2. "t)ber die Tafel primitiver Wurzeln," Jn. f. d. reine u. angew. Math., v. 45, 1853, p. 55-81. [di, 55: d3, 56-81.] 3. Magnus Canon Divisorum pro Omnibus Numeris per 2, 3, et 5 non Divisi- bilibus, et numerorum primorum interjacentiunt ad Millies centena milia accuratis ad 100 330 201 usque, 8 manuscript volumes, deposited in the Vienna Academy of Sciences in 1867, the second of which was missing in 1911. [e,.] Kulik had died in 1863. Accounts of this manuscript have been given by J. Petzval in Akad. d. Wiss., Vienna, math.-natw. Kl., Sitzungsb., v. 53, 1866, p. 460-462; and by D. N. LEHMER l.cols. IX, X, XIII, XIV, and D. N. LEHMER 2, cols. XI, XII. A photostatic copy of that part of Kulik's table which extends from 9 000 000 to 12 642 600 is in the possession of D. H. Lehmer. C. A. LAISANT. 1. "Les deux suites fibonacciennesfondamentales («„), (»„). Table de leurs termes jusqu' a n= 120," Enseignement Math., v. 21, 1920, p. 52-56. [b6, 53-56.] F. LANDRY. 1. Dfcom position des N ombres 2"+ 1 en leurs Facteurs Premiers de n= 1, a « = 64, mains quatre, Paris, 1869, 8 p. [e2, 6-7.] Libraries: RPB H. P. LAWTHER. 1. "An application of number theory to the splicing of telephone cables," Am. Math. Mo., v. 42, 1935, p. 81-91. [d4, 90.] V. A. LEBESGUE. li. Tables Diver ses pour la Decomposition des N ombres en leurs Facteurs Premiers, Paris, 1864, 37 p. [d, 18-37: fi, 12.] Libraries: CU, MH, MiU, RPB I2. So. d. Sci. Phys. et Nat. d. Bordeaux, Mtmoires, v. 3,1864, p. 1-37. [ei, 18-37 :fi, 12.] 2. "Tables donnant pour la moindre racine primitive d'un nombre premier ou puissance d'un premier: 1° les nombres qui correspondent aux in- dices: 2° les indices des nombres premiers et inferieurs au module," [com- puted by Hotiel]. So. d. Sci. Phys. et Nat. d. Bordeaux, Memoires, v. 3, 1864, p. 231-274. [c, 271-274: d3, 260-274.] E. LEBON. 1. Table de Caracteristiques de Base 30 030 donnant, en un seul Coup d'Oeil, [109]

LEG-LEH BIBLIOGRAPHY les Facteitrs Premiers des Nombres Premiers avec 30 030 et Inferieurs d, 901 800 900, v. 1, pt. 1, Paris, 1920, xxii+56 p. [e,, 1-56.] Libraries: ICJ, MH, NhD, NjP, NN, NNC, RPB, WU A. M. LEGENDRE. li. Essai sur la Theorie des Nombres, Paris, 1798, xxiv+472 p. + app. [fi, 17: i3*, Tables III-VII: ji*, Table XII: n, Tables I-XL] Libraries: CU, CaTU, ICU, InU, MB, MH, NNC, PU, RPB l». Second ed., Paris, 1808, xxiv+480 p.+app. [fi, Table IX: b*, Tables III-VII: ji, Table X: n, Tables I-VIIL] Libraries: CPT, CtY, DLC, ICU, IEN, laAS, MB, MCM, MH, NJP, NN, NNC, OCU, PEL, RPB, TxU 13. Third ed., Paris, 1830, v. 1, xxiv+396 p.+app. [fi, Table IX: is*, Tables III-VII: ji*, Table X: n, Tables I-VIII.] Libraries: InU, MdBJ, MB, MH, NhD, NcD, PU, RPB It. Fourth ed., Paris, 1900, identical with the third. Libraries: CU, CaM, ICU, IU, MH, MiU, MnU, NNC, RPB, WU l6. Zahlentheorie, German transl. of third ed. by H. MASER, Leipzig, 1886, v. 1, xviii+442 p. ft, 429: i,, 394-414: ji, 430-441: n, 390-428.] Libraries: DLC, MH, MiU, RPB 1«. Second German ed., identical with first except for title-page, 1893. Libraries: laAS, laU, OCU D. H. LEHMER. 1. "The mechanical combination of linear forms," Am. Math. Mo., v. 35, 1928, p. 114-121. [i2, 121.] 2. "On the multiple solutions of the Pell equation," Annals of Math., v. 30, 1928, p. 66-72. [e2, 72: ji, 72.] 3. "On the factorization of Lucas functions," Tdhoku Math. Jn., v. 34, 1931, p. 1-7. [o, 2-3.] 4. "Note on Mersenne numbers," Am. Math. So., Bull., v. 38, p. 383-384, 1932. [e,*.] 5. "On a conjecture of Ramanujan," London Math. So., Jn., v. 11, 1936, p. 114-118. [qi*, 117-118.] 6. "On the converse of Fermat's theorem," Am. Math. Mo., v. 43, 1936, p. 347-354. [d,, 349-351: g, 349-351.] 7. "On the function x*+x+A," Sphinx, Brussels, v. 6, 1936, p. 212-214. P..] 8. Solutions of ax*-\-bx-\-c=y* (mod p"). Manuscript in the possession of the author, [ii.] 9. Tables of solutions of x*-Dy*= + 1,1700 <Z>g 2000. Manuscript in the possession of the author, [ji.] 10. Table of factors of k2a— 1. Manuscript in possession of the author. [e2.] 11. "A list of errors in tables of the Pell equation," Am. Math. So., Bull., v. 32, 1926, p. 545-550. D. H. and E. T. LEHMER. 1. Waring Table of Fourth Powers, Berkeley, 1928, 436 p. Mimeographed. [110]

BIBLIOGRAPHY LEH-LIT [qs.] Only ten copies made. Libraries: RPB, The Carnegie Institution D. N. LEHMER. 1. Factor Table for the First Ten Millions containing the Smallest Factor of Every Number Not Divisible by 2, 3, 5, or 7 between the Limits 0 and 10 017 000 (Carnegie Inst. Publ. 105), Washington, 1909, x+478 p. [e..] Libraries: CPT, CU, CaM, CaTU, CoU, CtY, DLC, ICJ, ICU, IEN, IU, InU, laAS, laU, KyU, MdBJ, MB, MCM, MH, MiU, MnU, MoU, NhD, NjP, NN, NNC, NRU, NcD, OU, PEL, PU, RPB, WvU, WU 2. List of Prime Numbers from 1 to 10 006 721 (Carnegie Inst. Publ. 165), Washington, 1914, xvi+133 p. [fi*.] Libraries: CPT, CU, CaM, CaTU, CoU, CtY, DLC, ICJ, ICU, IEN, IU, InU, laAS, laU, KyU, MdBJ, MB, MCM, MH, MiU, MnU, NhD, NjP, NN, NNC, NRU, NcD, OCU, OU, PEL, PU, RPB, TxU, WU 3i. Factor Stencils, (Carnegie Inst.), Washington, 1929, 24 p. +295 stencils [f,:g:is.]* Libraries: CPT, CtY, ICJ, IU, InU, laU, MdBJ, MH, NhD, NjP, OCU, PBL, PU, RPB 32. Factor Stencils, revised and extended by J. D. ELDER, (Carnegie Inst.), Washington, 1939, 27 p. +2135 stencils. [f2: g: i,.] Libraries: CPT, CU, ICJ, IU, NhD, NjP, NNC, PU, RPB 4. Table of linear divisors of x* — Dy* for \D\ <317. Manuscript in the possession of Prof. D. H. LEHMER. [ia.] E. T. LEHMER. [See also D. H. and E. T. LEHMER.] 1. "Note on Wilson's quotient," Am. Math. Mo., v. 44, 1937, p. 237-238. [b,.] 2. "Terminaisons des carres dans la base 12 et autres bases," Sphinx, Brussels, v. 9, 1939, p. 51-54. [i,, 51.] W. LENHART. 1. "Useful tables relating to cube numbers," Math. Miscellany (Gill), sup- plement to v. 1, 1838, p. 1-16. [1.] S. LEVANEN. 1. "Om talens delbarhet," [On the divisibility of numbers], Finska Vetens- kaps-Societeten, Ofversigt af Forkandlingar, v. 34, p. 109-162, 1891-2. [ds, 138-161.] 2. "En metod for upplosande af tal i factorer," Finska Vetenskaps-So- cieteten, Ofversigt af Forhandlingar, v. 34, p. 334-376, 1892. [is*, 356- 370.] N. J. LlDONNE. 1. Tables de Tous les Diviseurs des Nombres calculies depuis unjusqu'd cent deux mille, Paris, 1808, 39+ccxviii p. [d, i-cxxxi.] Libraries: NNC, RPB J. E. LITTLEWOOD, see HARDY and LITTLEWOOD. [Ill]

LOD-MAT BIBLIOGRAPHY A. LODGE, see MILLER and LODGE; also PETERS, LODGE and TERNOUTH, GLFFORD. £. LUCAS. 1. Th6orie des fonctions numeriques simplement periodiques," Am. Jn. Math., v. 1, 1878, p. 184-239, 289-321. [e,, 294-299.] 2. "Sur les formules de Cauchy et de Lejeune Dirichlet," Ass. Franc, pour 1'Avan. d. Sci., Comptes Rendus, v. 7, p. 164-173, 1878. [o*, 165, 168.] 3. "Sur la serie recurrente de Fermat," Bullettino d. Bibliografia e d. Storia (Boncompagni), v. 11, 1878, p. 783-798. [o*, 786.] 4. "Sur la theorie des fonctions numeriques simplement periodiques," Nouv. Corresp. Math., v. 4, 1878, p. 33-40. [is, 38-39.] 5. Theorie des Nombres, Paris, 1891, xxxiv+520 p. [bi, 395.] Libraries; CPT, CU, CaM, CaTU, CoU, CtY, 1C], ICU, IEN, IU, InU, laAS, IaU, KyU, MdBJ, MB, MH, MiU, MoU, NhD, NjP, NN, NNC, NRU, NcD, OCU, OU, PEL, PU, RPB, TxU, WU P. A. MACMAHON. [See also HARDY and RAMANUJAN 1.] 1. "The parity of p(n) the number of partitions of n, when «^1000," London Math. So., Jn., v. 1, 1926, p. 226. [qi.] A. MARKOV. 1. "Table des formes quadratiques ternaires indefinies ne representantes pas zero pour tous les determinants positifs D^50," Akad. Nauk S.S.S.R., Leningrad, d. phys.-math., Memoires, s. 8, v. 23, no. 7, 1909, 22 p. [n.] A. MARTIN. 1. "Rational scalene triangles," Math. Magazine, v. 2, p. 275-284, 1904. [j», 284.] 2. "Table of prime rational right-angled triangles," Math. Magazine, v. 2, p. 297-324, 1910. [Js, 301-308, 322-323.] 3. "On rational right-angled triangles," Int. Congress Mathems., Cam- bridge, 1912, Proc., v. 2, Cambridge, 1912, p. 40-58. [J3,57-58.] T. E. MASON. [See also CARMICHAEL and MASON.] 1. "On amicable numbers and their generalizations," Am. Math. Mo., v. 28, 1921, p. 195-200. [a, 196-197.] G. B. MATHEWS. 1. Theory of Numbers, Cambridge, Part I, 1892, vii+323 p. [g, 263: o, 218.] Facsimile reprint, New York, 1927. Libraries: CPT, CU, CaM, CaTU, CoU, CtY, ICJ, ICU, IEN, IU, INU, laAS, IaU, MdBJ, MB, MCM, MH, MiU, MnU, NhD, NjP, NN, NNC, OCU, OU, PEL, PU, RPB, WvU. WU 2. "On the reduction and classification of binary cubics which have a nega- tive discriminant," London Math. So., Proc., s. 2, v. 10, 1912, p. 128- 138. [n, 137-138.] [112]

BIBLIOGRAPHY MAT-NAG I. V. MATIES. 1. "Terminatiunile cuburilor perfecte si a radacinilor lor," [Endings of per- fect cubes and their roots], Gazeta Mat., v. 41, 1936, p. 332-338. [d6, 336.] M. E. MAUCH. 1. Extensions of Waring's theorem on seventh powers (Doctoral diss; Chicago), Chicago, 1938, iii+21 p. Manuscript. [qs.] Libraries: ICU W. MEISSNER. 1. "Ueber die Teilbarkeit von 2"—2 durch das Quadrat der Primzahl />=1093,'' Akad. d. Wiss., Berlin, Sitzungsb., v. 35, 1913, p. 663-667. [b4, 666-667: d2, 666-667.] 2. "Ueber die Losungen der Kongruenz x"~i = l (mod pm) und ihre Ver- wertung zur Periodenbestimmung mod pk," Berliner Math. Gesell., Sitzungsb., v. 13, 1914, p. 96-107. [d4, 104-105.] C. W. MERRIFIELD. 1. "The sums of the series of the reciprocals of the prime numbers and of their powers," Royal So. London, Proc., v. 33, 1881, p. 4-10. [fi*, 10.] F. MERTENS. 1. "Uber eine zahlentheoretische Function," Akad. d. Wiss., Vienna, math.-natw. Kl., Sitzungsb., 2a, v. 106, 1897, p. 761-830. [b3, 781-830.] J. C. P. MILLER. 1. "Table of the inverse totient function," manuscript table in possession of the author, [bi.] J. C. P. MILLER and A. LODGE. 1. "Super- and sub-multiples," manuscript tables in possession of J. C. P. Miller. [e2.] N. B. MITRA. 1. "The converse of Fermat's theorem," Indian Math. So., /«., v. 15, 1923, p. 62-68. [de, 64-66.] C. MOREAU. 1. "Sur quelques theoremes d'arithmetique," Now. Annales d. Math., s. 3, v. 17, 1898, p. 293-307. [bi, 303-307.] R. E. MORITZ. 1. "The sum of products of n consecutive integers," Univ. of Wash., Publ. Math., v. 1, no. 3, 1926, p. 29-49. [b6, 44-49.] T. NAGELL. 1. "Uber die Losbarkeit der Gleichung xt-Dy*=-l,n Arkiv. f. Mat., Astronomi och Fysik, v. 23, no. 6, 1933, p. 1-5. [ji, 2.] [113]

NIE-PER BIBLIOGRAPHY N. NIELSEN. 1. "Recherches sur certaines equations de Lagrange de formes speciales," K. Danske Vidensk. Selskab, Copenhagen, Math.-fysiske Meddelelser, v. 5, no. 4, 1923, p. 1-95. [ji, 87-93: J2, 87-93: m, 90-93.] 2. "Sur le genre de certaines equations de Lagrange," K. Danske Vidensk. Selskab, Copenhagen, Math.-fysiske Meddelelser, v. 5, no. 5, 1923, p. 1- 72. [j,, 58-72.] 3. "Sur 1'op6ration iterative des Equations de Lagrange," K. Danske Vidensk. Selskab, Copenhagen, Math.-fysiske Meddelelser, v. 6, no. 1, 1924, p. 1-98. [j2. 85-96.] 4. Tables Numeriques des Equations de Lagrange, Copenhagen and Paris, 1925, xvii+400 p. [js.] Libraries: CPT, CU, CtY, laAS, NjP, RPB 5. Recherches Numeriques sur Certaines Formes Quadratiques, Copenhagen, 1931,xi+160p. [j2.] Libraries: CPT, CU, DLC, ICJ, ICU, IU, laU, MH, MiU, NjP, NN, RPB R. NlEWIADOMSKI. 1. "Zur Fermatschen Vermutung," Prace Mat. Fiz., v. 42,1935, p. 1-10., [de.] L. OETTINGER. 1. "tJber das Pell'sche Problem und einige damit zusammenhangende Probleme aus der Zahlenlehre," Archiv. Math. Phys., v. 49,1869, p. 193- 222. [J2, 217-222:1, 221-222.] M. OSTROGRADSKY. 1. "Tables des racines primitives pour tous les nombres premiers au des- sous de 200, avec les tables pour trouver 1'indice d'un nombre donne, et pour trouver le nombre d'apres 1'indice," Akad. Nauk S.S.S.R., Leningrad, Memoires . . . Sci. math., phys. et nat., s. 6, v. 1, 1838, p. 359-385. [di:ds.]* G. PAGLIERO. 1. "I numeri primi da 100 000 000 a 100 005 000," R. Accad. d. Sci. d. Torino, Atti, v. 46, 1911, p. 766-770. [tf, 769.] G. PALL, see JONES and PALL. C. G. PARADINE. 1. Table of 1120 triangles with integral sides, and at least one integral median. Manuscript in the possession of the author. [js.] J. PEROTT. 1. "Sur la sommation des nombres," Bull. d. Sci. Math., s. 2, v. 5, pt. 1, 1881, p. 37-40. [b,, 39-40.] O. PERRON. li. Die Lehre von den Kettenbriichen, Leipzig and Berlin, 1913, xii+520 p. [ji, 101 :m, 101.] [114]

BIBLIOGRAPHY PET-POL Libraries: CPT, CU, CoU, CtY, DLC, ICU, IEN, IU, InU, laU, KyU, MdBJ, MH, MiU, MoU, NhD, NjP, NN, NNC, OU, PEL, PU, RPB, TxU, WU I2. Second ed., Leipzig and Berlin, 1929, xii+524 p. [j,, 101: m, 101.] Libraries: CPT, CaTU, CtY, ICU, IU, laAS, MdBJ, MCM, MH, MiU, MnU, NjP, NNC, NRU, NcD, OCU, PU, RPB, WU J. PETERS, A. LODGE and E. J. TERNOUTH, E. GIFFORD. 1. Factor Table Giving the Complete Decomposition of all Numbers less than 100 000 (Br. Ass. Mathematical Tables, v. 5), London, 1935, xv+291 p. [d, 2-288: g, 285-291.] Libraries: CU, IU, NNC, RPB J. PETERS and J. STEIN. 1. Anhang to J. Peters' Zehnstellige Logarithmentafel, v. 1, Berlin, 1922, [separate pagination], xxviii+195 p. [e2, 75-82.] Libraries: CU, RPB S. S. PlLLAI. 1. "On Waring's problem," Indian Math. So., Jn., n.s., v. 2,1936, p. 16-44. [q,, 40-44.] N. PIPPING. 1. "Neue Tafeln fur das Goldbachsche Gesetz nebst Berichtigungen zu den HaussnerschenTafeln," Finska Vetenskaps-Societeten, Commentationes physico-math., v. 4, no. 4, 1927, 27 p. [q2, 7-23, 25.] 2. "Uber Goldbachsche Spaltungen grosser Zahlen," Finska Vetenskaps- Societeten, Commentationes physico-math., v. 4, no. 10, 1927, 15 p. [q2, 12-14.] 3. "Die Goldbachschen Zahlen G(x) fur *=120 072-120 170," Finska Vetenskaps-Societeten, Commentationes physico-math., v. 4, no. 25,1929, 6 p. [q2.] 4. "Die Goldbachsche Vermutung und der Goldbach-Vinogradowsche Satz," Abo, Finland, Akademi, Acta Math, et Phys., v. 11, no. 4, 1938, p. 1-25. [q2, 9-25.] H. C. POCKLINGTON. 1. "An algebraical identity," Nature, v. 107, 1921, p. 587. [o.] L. POLETTI. [See also BEEGER 8.] 1. Resultati Teorico-Pratici di una Radicals Modificazione del Crivello di Eratostene, Parma, 1914, 47 p. [fi, 31-47.] Libraries: CU 2. Tavole di Numeri Primi entro Limiti Diversi e Tavole Affini, Milan, 1920, xx+294 p. [ei*, 120-186: f,*, 3-118, 235-247: f,, 249-255.] Libraries: CU, ICU, MdBJ, MiU, NjP, NNC, RPB, WU 3. "Liste des nombres premiers de la forme quadratique 5«2+5«+l de «= 1415-2200," NieuwArchiefv. Wiskunde, s. 3, v. 16,pt. 2,1929, p. 27- 30. [f,.] [115]

POL-POU BIBLIOGRAPHY 4. "Le serie dei numeri primi appartenente alle due forme quadratiche (A) «2+«+l e (B) «2+«—1 per 1'intervallo compreso entro 121 mil- lioni, e cioe per tutti i valori di n fino a 11000," R. Accad. Naz. d. Lincei, Cl. d. sci.fis., mat. e. nat., Memorie, s. 6, v. 3, 1929, p. 193-218. [ft, 197- 218.] 5. "Elenco di numeri primi fra 10 milioni e 500 milioni estratti da serie quadratiche," R. Accad. d'ltalia, Rome, Cl. d. sci. fis., mat. e nat., Memorie, Matematica, v. 2, no. 6, 1931, p. 5-107. [f,, 22-107.] 6. "Atlante di oltre 60 000 numeri primi fra 10 milioni e tre miliardi stratti da serie quadratiche." Manuscript deposited with Consiglio Nazionale delle Ricerche Pratiche in Rome, [f^.] 7. List of primes between 107 and 2-10'represented by «2+«+a, a = 19421, 27 941, 72 491. Manuscript in possession of the author, and D. H. Lehmer. [f2.] L. POLETTI and E. STURANI. 1. "Le serie dei numeri primi entro i primi centomilia n. succ. oltre cento milioni, e le serie dei n.p.da 14285717 a 14 299 991.—Quadri sinottici sui fenomeni di frequenza dei n.p. entro i primi centomilia n. succ. della serie naturale situati oltre 0, 10, 100,1000 milioni," R. Ist. Lombardo d. Sci. e Lettere, Rendiconti, v. 61, 1928, p. 140-176. [fi.] 2i. "Le serie dei numeri primi appartenenti alle due forme quadratiche (2«2+2«- I)e(2«2+2«+l) entro 250 milioni, "Int. Congress Mathems. Bologna, 1928, Atti, v. 2, Bologna, 1928, p. 113-133. [f2, 119, 122-133.] 22. [Same title], R. Ist. Lombardo d. Sci. e Lettere, Rendiconti, v. 62, 1929, p. 723-759. [f2, 737-759.] K. POSSE. 1. "Tablitsapervoobraznykh kornei ikharakterov k nim otnosiashchikhsia, dlia prostykh chisel mezhdu 4000 i 5000," [Table of primitive roots and of characters pertaining to them for prime numbers between 4000 and 5000], Matematicheskil Sbornik, v. 27, 1909, p. 175-179. [dk: da: e,.] _ 2. "Tablitsa pervoobraznykh kornei i kharakterov k nim otnosiashchikhsia, dlia prostykh chisel mezhdu 5000 i 10000," [Table of primitive roots and of characters pertaining to them for prime numbers between 5000 and 10000], Matematicheskil Sbornik, v. 27, 1909, p. 238-257. [di: d3: C2.] 3. "Expose succinct des resultats principaux du memoire posthume de Korkine, avec une table des racines primitives et des caracteres, qui s'y rapportent, calculee par lui pour les nombres premiers inf6rieurs a 4000 et prolongee jusqu' a 5000," Acta Math., v. 35, 1911-12, p. 193- 231. [di: d3: e2.] 4. "Table des racines primitives et des caracteres qui s'y rapportent pour les nombres premiers entre 5000 et 10000," Acta Math.,v. 35,1911-12, p. 233-252. [di:d3:e2.] P. POULET. 1. "Note sur les multiparfaits," Sphinx Oedipe, v. 20,1925, p. 2-4, 85-93. [a.] [116]

BIBLIOGRAPHY RAM-ROB 2. La Chasse aux Nombres, v. 1, Brussels, 1929, 72 p. [a*, 14-25,46-50, 53- 65,68-72.] Libraries: RPB 3. La Chasse aux Nombres, v. 2, Brussels, 1934, 188 p. [b«, 38-51, 94-109, 168-184: et, 38-51, 94-109, 168-184: o, 161.] Libraries: RPB 4i. "Table des nombres composes v6rifiant le theoreme de Fermat pour le module 2 jusqu'a 100 000 000," Deuxieme Congres Int. d. Recreation Math., Comptes Rendus, Brussels, 1937, p. 74-84. [d«, 77-84: g, 77-84.]* 42. [Reprinted in] Sphinx, Brussels, v. 8, 1938, p. 42-52. [d«: g.]* 5. "Des nouveaux amiables," Sphinx, Brussels, v. 4, 1934, p. 134-135. [a.] S. RAMANUJAN. [See also HARDY and RAMANUJAN.] h. "Highly composite numbers," London Math. So., Proc., s. 2, v. 14,1915, p. 347-409. [b,*, 358-360.] I2. Collected Papers, Cambridge, 1927, p. 78-128. [b2, 87-88.] Libraries: CPT, CU, CaM, CoU, CtY, DLC, ICU, IU, laAS, laU, MdBJ, MCM, MH, MiU, NhD, NjP, NN, NcD, OCU, OU, PU, RPB, WU 2i. "On certain arithmetical functions," Cambridge Phil. So., Trans., v. 22, no. 9, 1916, p. 155-184. [q,, 174.] 2t. Collected Papers, 1927, p. 136-162. [qi, 153.] L. W. REID. 1. Tafel der Klassenanzahlen fur kubische Zahlkorper (Diss. Gottingen), Gottingen, 1899, viii+76 p. [p, 12, 60-75.] Libraries: CU, CtY, MH, NjP, NNC, NIC, OCU, PU, RPB 2. "A table of class numbers for cubic number fields," Am. Jn. Math., v. 23, 1901, p. 68-84. [p, 75-84.] K. G. REUSCHLE. 1. Mathematische Abhandlung, enhaltend: Neue Zahlentheoretische Tabellen (Programm), Stuttgart, 1856, 61 p. [di*, 42-53:dt*, 42-61: d6, 23-41: 62*, 18-22, 42-61: f2, 23-28, 32-38: j,*, 23-41.] Libraries: DLC, NNC, RPB 2. [Tables of the decomposition of primes into complex factors], Preuss. Akad. d. Wiss., Monatsberichte, 1859, p. 488-491, 694-697; 1860, p. 90- 199, 714-735. [p.] 3. Tafeln Complexer Primzahlen welche aus Wurzeln der Einheit gebildet sind, Berlin, 1875, vi+671 p. [d4: k: o: p.]* Libraries: CtY, ICU, IU, MdBJ, MH, MiU, NhD, NjP, PU, RPB H. W. RICHMOND. 1. "On integers which satisfy the equation t3 + x* ± y3 + 2' = 0," Cambridge Phil. So., Trans., v. 22, p. 389-403, 1920. [1, 402.] C. A. ROBERTS. 1. "Table of the square roots of the prime numbers of the form 4>w+1 less [117]

ROB-SEE BIBLIOGRAPHY than 10 000 expanded as periodic continued fractions," Math. Maga- zine, v. 2, p. 105-120, 1892. [m*, 106-120.] R. M. ROBINSON. 1. Stencils for solving x* = a (mod m), Berkeley 1940, 14 p. [ii.] A. E. Ross. [See also DICKSON 6.] 1. Quadratic form tables. Manuscript tables produced under the direction of A. E. Ross, Number Theory Laboratory, St. Louis University. (Available in microfilm.) [n.] E. SANG. 1. "On the theory of commensurables," Royal So. Edinburgh, Trans., v. 23, 1864, p. 721-760. [j3*, 757-760.] —. SAOKGIO. 1. "Sur le probleme, un nombre entier etant donne pour 1'un des cdtes d'un triangle rectangle trouver toutes les couples des nombres aussi entiers qui avec le cote donne forment ce triangle," R. Accad. d. Sci. d. Torino, Memorie, v. 6, 1792, p. 239-252. [J3, 243-245.] L. SAPOLSKY, see ZAPOLSKAIA. M. L. N. SARMA. 1. "On the error term in a certain sum," Indian Acad. Sci., Proc., s. A., v. 3,1936, p. 338. [bf, 338.] —. SCHADY. 1. "Tafeln fur die dekadeschen Endformen der Quadratzahlen," Jn. /. d. reine u. angew. Math., v. 84, 1878, p. 85-88. [h, 87-88.] K. SCHAFFSTEIN. 1. "Tafel der Klassenzahlen der reellen quadratischen Zahlkorper mit Primzahl Diskriminante unter 12 000 und zwischen 100 000-101 000 und 1 000 000-1 001 000," Math. Ann., v. 98, 1928, p. 745-748. [p.] H. F. SCHERK. 1. "Bemerkungen iiber die Bildung der Primzahlen aus einander," Jn.f. d. reine u. angew. Math., v. 10, 1833, p. 201-208, 292-293. [f2, 208: qt, 292- 293.] J. C. SCHULZE. 1. Neue und Erweiterte Sammlung Logarithmischer, Trigonometrischer und Anderer zum Gebrauch der Mathematik U nentbehrlicher Tafeln, Berlin, 1778, v. 2, 49+319 p. [js*, 308-311.] Libraries: ICU, IEN, MiU, NjP, NN, NNC, PEL, RPB L. A. SEEBER. 1. Untersuchungen iiber die Eigenschaften der Positiven Terndren Quad- ratischen Formen, Freiburg, 1831, 248 p. [n, 220-243.] Libraries: NN [118]

BIBLIOGRAPHY SEE-SOM P. SEELHOFF. 1. "Priifung grosserer Zahlen auf ihre Eigenshaft als Primzahlen," Am. Jn. Math., v. 7, 1885, p. 264-269, [g, 267-269: n, 267-269]; v. 8, 1886, p. 26-38, [g, 29-38: n, 29-38]. P. SEELING. 1. "Verwandlungder irrationalen Grosse -\Xin einen Kettenbruch," Archiv Math. Phys., v. 46, 1866, p. 80-120". [m, 102-120°.] 2. "Ueber periodische Kettenbriiche fiir Quadratwurzeln," Archiv Math. Phys., v. 49, 1869, p. 4-44. [m, 24-38.] 3. "Ueber die Auflosung der Gleichung x*—Ay*= + 1 in ganzen Zahlen," Archiv Math. Phys., v. 52, 1871, p. 40-49. [j^ 48-49.] N. M. SHAH and B. M. WILSON. 1. "On an empirical formula connected with Goldbach's theorem," Cam- bridge Phil. So., Proc., v. 19, 1919, p. 238-244. [q2, 240.] W. SHANKS. 1. "On the number of figures in the period of the reciprocal of every prime number below 20 000," Royal So. London, Proc., v. 22, 1874, p. 200- 210. [d2*, 203-210.] 2. "Given the number of figures (not exceeding 100) in the reciprocal of a prime number, to determine the prime itself," Royal So. London, Proc., v. 22, 1874, p. 381-384. fa.] 3. "On the number of figures in the period of the reciprocal of every prime number between 20 000 and 30 000," Royal So. London, Proc., v. 22, 1874, p. 384-388. [d2*, 385-388.] 4. "On the number of figures in the period of the reciprocal of every prime between 30 000 and 120 000," Manuscript table deposited in the Archives of the Royal Society of London (see CUNNINGHAM 40, p. 148- 149). [d,.] R. C. SHOOK. 1. Concerning Waring' s Problem for Sixth Powers (Diss. Chicago), Chicago, 1934,ii+38p.[q,.] Libraries: CU, CaM, CaTU, CoU, DLC, ICJ, ICU, IEN, IU, laU, MdBJ, MH, MiU, MnU, MoU, NjP, NN, NNC, NcD, OCU, OU, RPB, TxU W. SlMERKA. 1. "Die rationalen Dreiecke," Archiv Math. Phys., v. 51, 1870, p. 196-241. [j,, 225-240.] 0. SIMONY. 1. "tiber den Zusammenhang gewisser topologischer Thatsachen mit neuen Satzen der hoheren Arithmetik und dessen theoretische Bedeut- ung," Akad. d. Wiss., Vienna, math.-natw. Kl., Sitzungsb., v. 96, 1887, p. 191-286. [f,, 218-224, 252-280.] 1. S. SOMINSKII, see DELONE, SOMINSKII and BILEVICH. [119]

SOM-STER BIBLIOGRAPHY J. SOMMER. li. Vorlesungen uber Zahlentheorie, Leipzig and Berlin, 1907, vi+361 p. [p*, 346-361.] Libraries: CPT, CU, CtY, ICJ, ICU, IEN, IU, MdBJ, MH, MiU, MoU, NhD, NjP, NN, OCU, PU, RPB, WU Is. Introduction d la Theorie des Nombres Algebriques, French transl., re- vised and augmented, by A. LEVY, Paris, 1911, x+376 p. [p*, 361-373.] Libraries: CU, CaTU, CoU, CtY, ICU, IU, InU, MiU, NjP, NN, NNC, OU, PU, RPB, TxU F. W. SPARKS. 1. Universal Quadratic Zero Forms in Four Variables (Diss. Chicago), Chi- cago, 1931, i+49 p. [q3.] Libraries: CU, CoU, CtY, DLC, ICJ, ICU, IEN, IU, laU, KyU, MdBJ, MH, MiU, MnU, MoU, NjP, NN, NNC, NcD, OCU, OU, PU, RPB, TxU, WU P. STACKEL. 1. "Die Liickenzahlen r-ten Stufe und die Darstellung der geraden Zahlen als Summen und Difierenzen ungerader Primzahlen," Heidelberger Akad. d. Wiss., Sitzungsb., math.-natw. Kl., 1917, no. I5, 52 p. [fb 29: q» 52.] H.W. STAGER. 1. "On numbers which contain no factors of the form />(£/>+1)," Calif., Univ., Publ. in Math., v. 1, no. 1, 1912, p. 1-26. [ft, 19-26.] 2. A Sylow Factor Table of the First 12 000 Numbers, giving the Possible Number of Sylow Subgroups of a Group of Given Order between the Limits 0 and 12 000 (Carnegie Inst. Publ. 151), Washington, 1916, xii+120p. [d, 1-120: fi, x-xii.] Libraries: CPT, CU, CaTU, CoU, CtY, DLC, ICJ, ICU, IEN, IU, InU, laAS, laU, KyU, MdBJ, MB, MCM, MH, MiU, MnU, MoU, NhD, NjP, NN, NNC, NRU, NcD, OCU, OU, PBL, PU, RPB, TxU, WvU, WU J. STEIN, see PETERS and STEIN. R. D. VON STERNECK. 1. "Empirische Untersuchung liber den Verlauf der zahlentheoretischer Function v(n)= 2".in(x) im Intervalle von 0 bis 150 000," Akad. d. Wiss., Vienna, math.-natw. Kl., Sitzungsb., 2 a, v. 106,1897, p. 835-1024. [b3*, 843-1024.] 2. "Empirische Untersuchung iiber den Verlauf der zahlentheoretischer Function <r(n) = S £-i/»(*) im Intervalle von 150 000 bis 500 000," Akad. d. Wiss., Vienna, math.-natw. Kl., Sitzungsb., v. 110, section 2a, 1901, p. 1053-1102. [bs, 1059-1102.] 3. "Uber die kleinste Anzahl Kuben aus welchen jede Zahl bis 40 000 zusammengesetzt werden kann," Akad. d. Wiss., Vienna, math.-natw. Kl., Sitzungsb., v. 112, section 2a, 1903, p. 1627-1666. [q3*, 1640-1666.] 4. "Die zahlentheoretische Function <r(n) bis zur Grenze 5 000 000," [120]

BIBLIOGRAPHY STI-SYL Akad. d. Wiss., Vienna, math.-natw. Kl., Sitzungsb., 2 a, v. 121,1912, p. 1083-1096. [bs, 1085.] 5. "Neue empirische Daten iiber die zahlentheoretische Function <r(n)," Int. Congress Mathems., Cambridge, 1912,Proc.,v. 1, Cambridge, 1912, p. 341-343. [b3, 342.] T. J. STIELTJES. li. "Bijdrage tot de theorie der derde- en vierde-machtsresten," Akad. v. Wetensch., Amsterdam, Verslagen, afdeeling natuurkunde, sect. 1, s. 2, v. 17, 1882, p. 338-417. [d6, 396-397.] U. French transl., "autorise'e par 1'auteur": "Contribution a la theorie des residus cubiques et biquadratiques," Archives N eerlandaises d. Sci. Exactes et Nat., The Hague, v. 18, 1883, p. 358-436. [d6, 415-416.] l8. Oeuvres, Groningen, v. 1, 1914, p. 145-209. [dB, 192-193.] (French transl. p. 210-275. [dB, 257-258.]) E. STORANI, see POLETTI and STURANI. E.SUCHANEK. 1. "Dyadische Coordination der bis 100 000 vorkommenden Primzahlen zur Reihe der ungeraden Zahlen," Akad. d. Wiss., Vienna, math.-natw. Kl., Sitzungsb., v. 103, 1894, p. 443-610. [fi, 452-554.] A. SUGAR. 1. A new universal Waring theorem for eighth powers (Master's thesis, Chicago), Chicago, 1934, iii+l0p. Manuscript. [q3.] Libraries: ICU M. SURYANARAYANA. 1. "Positive determinants of binary quadratic forms whose class number is 2," Indian Acad. Sci., Proc., s. A, v. 2, 1935, p. 178-179. [n.] C. S. SUTTON. 1. "An investigation of the average distribution of twin prime numbers," Jn. of Math, and Physics, Mass. Inst. Tech., v. 16,1937, p. 1-42. [fi, 4-6, 34-42.] J. J. SYLVESTER. 1i. "On certain ternary cubic-form equations," Am. Jn. Math., v. 2, 1879, p. 280-285, 357-393; v. 3, 1880, p. 58-88, 179-189. [o*, 367-368, 380.] 12. Collected Papers, Cambridge, v. 3, 1909, p. 312-391. [o, 326-327, 338.] 2i. "On the number of fractions contained in any 'Farey Series' of which the limiting number is given," Phil. Mag., v. 15,1883, p. 251-257; v. 16, 1883, p. 230-233. [b?.] 2». Collected Papers, v. 4,1912, p. 101-109. [bi, 103-109.] Libraries: v. 3, 4, CPT, CU, CaM, CaTU, CoU, CtY, DLC, ICJ, ICU, IU, InU, laAS (not v. 4), laU, KyU, MdBJ, MB, MCM, MH, MiU, MnU, NliD, NjP, NN, NNC, NcD, OCU, OU, PU, RPB, TxU, WU [121]

TAI-UME BIBLIOGRAPHY P. G. TAIT. h. "On knots," Royal So. Edinburgh, Trans., v. 32, 1887, p. 327-342. [qi, 342.] 12. Scientific Papers, Cambridge, v. 1, 1898, p. 318-334. [qi, 334.] Libraries: CPT, CU, CaM, CaTU, CtY, DLC, ICJ, ICU, laU, MdBJ, MB, MH, MnU, MoU, NhD, NjP, NIC, NNC, NcD, OCU, OU, RPB, WvU, WU H. W. L. TANNER. 1. "On the binomial equation xv— 1=0: quinquisection," London Math. So., Proc., s. 1, v. 18, 1887, p. 214-234. [o, 229-230: p, 229-230.] 2. "Complex primes formed with the fifth roots of unity," London Math. So., Proc., s. 1, v. 24, 1893, p. 223-272. [j,, 256-262: p, 256-262.]* P. L. TCHEBYCHEF, SCC CHEBYSHEV. S. TEBAY. 1. Elements of Mensuration, London and Cambridge, 1868, viii+115 p. [j,Mii-IIs.] Libraries: MB, RPB H. TEEGE. 1. Ueber die (p—l)/2 gliedrigen Gausschen Perioden in der Lehre von der Kreisteilung und ihre Beziehungen zu anderen Teilen der Hoheren Arith- metik (Diss. Kiel), Kiel, 1900, 38 p. + app. [o*, app.] Libraries: CU, CtY, DLC, IU, MB, MnU, NjP, NN, NNC, OU, PU, RPB, WU E. J. TERNOUTH, see PETERS, LODGE and TERNOUTH, GIFFORD. G. S. TERRY, see E. T. LEHMER 2. V. THEBAULT. 1. "Sur les carres parfaits," Supplement to Mathesis, v. 48, Oct., 1934, 22 p. [is.] M. VON THIELMANN. 1. "Zur Pellschen Gleichung," Math. Ann., v. 95, 1926, p. 635-640. [m, 637-640.] S. B. TOWNES. 1. "Table of reduced positive quaternary quadratic forms," Annals of Math., v. 41, 1940, p. 57-58. [n.] J. TRAVERS. 1. "Perfect numbers," Math. Gazette, v. 23, 1939, p. 302. [a.] P. L. TSCHEBYSCHEW, SCC CHEBYSHEV. K. UMEDA. 1. "Zur Beziehung zwischen partitio numerorum und Kernanregung," [122]

BIBLIOGRAPHY USP-WER Tokyo, Inst. Physical and Chemical Research, Scientific Papers, v. 34, 1938, p. 629-636. [qi.] J. V. USPENSKY and M. A. HEASLET. 1. Elementary Number Theory, New York and London, 1939, x+484 p. [d,, 477-480.] Libraries: CPT, CU, CaTU, CoU, CtY, DLC, ICJ, ICU, IEN, IU, InU, laAS, laU, KyU, MB, MCM, MH, MnU, NhD, NjP, NN, NNC, NcD, OCU, RPB, WU L. VALROFF. 1. "Congruences 2x*- 1=0 (mod p)," SphinxOedipe, v. 9,1914, p. 73. [d4.] H. S. VANDIVER. 1. "On Bernoulli's numbers and Fermat's last theorem," Duke Math. Jn., v. 3, 1927, p. 569-584. [e2, 576.] G. VEGA. li. Sammlung Mathematischer Tafeln, Stereotyp-Ausgabe. Erster Abdruck [ed. by J. A. HULSSE], Leipzig, 1840, xxiii+681 p. [ei*, 360-423: fi*, 424-454.] Libraries: DLC, ICU, NN, NNC l». Zweiter Abdruck, Leipzig, 1849, xxiii+840 p. [d*, 360-423: fi*, 424-454.] Libraries: CU, CtY, MiU, NhD, OU, RPB A. VEREBRIUSOV. 1. "Equation ind6terrmnee," Ulntermedaire d. Math., v. 21, 1914, p. 153- 155. [1*, 154-155.] 2. "Ob uravnenii [on the equation] x4+y*+34 = at'4+y'4+s'4," Matemati- cheskit Sbornik, v. 30, 1916, p. 325-343. [1, 343.] G. F. VORONOl. 1. 0 tsiel'ikh algebraicheskikh chislakh zavisiashchikh ot kornia uraveneniia 3-1 stepeni, [On algebraic integers depending on a root of a cubic equation] (Master's diss. St. Petersburg), St. Petersburg, 1894, ix+158 +30 p. [p, app. 1-30.] Libraries: CU, ICU, MH, MoU, RPB G. N. WATSON. 1. "Two tables of partitions," London Math. So., Proc., s. 2, v. 42, 1937, p. 550-556. [qt.] W. WEINREICH, see STACKEL. G. WERTHEIM. 1. Elemente der Zahlentheorie, Leipzig, 1887, ix+381 p. [di, 116.] Libraries: CPT, CU, CaM, DLC, ICJ, ICU, IU, InU, laU, KyU, MH, MiU, MoU, NjP, NNC, PU, RPB, WU 2. "Tabelle der kleinsten primitiven Wurzeln g aller ungeraden Primzahlen p unter 3000," Acta Math., v. 17, 1893, p. 315-319. [di*.] [123]

WES-WOL BIBLIOGRAPHY 3. "Primitive Wurzeln der Primzahlen von der Form 2"q+l in welcher 9=1 oder eine ungerade Primzahl ist," Z. f. math. u. nat-w. Unterricht, v. 25, 1894, p. 81-97. [di, 97: f2, 84, 86-88, 90-91, 95-96.] 4. "Tabelle der kleinsten primitiven Wurzeln g aller Primzahlen p zwischen 3000 und 5000," Acta Math., v. 20, 1896-7, p. 153-157. [di*.] 5. Anfangsgrtinde der Zahlenlehre, Brunswick, 1902, xii+427 p. [di, 406- 411: d3, 412-419: h, 411: i2, 422: i3, 421: ji, 420.] Libraries: CU, CaM, CoU, ICJ, ICU, IU, MdBJ, MB, MH, MiU, MoU, NjP, NNC, RPB A. E. WESTERN. 1. "Note on the number of primes of the form «2+1," Cambridge Phil. So., Proc., v. 21, 1922, p. 108-109. [f2.] 2. "Computations concerning numbers represented by 4 or 5 cubes," Lon- don Math. So., Jn., v. 1, 1925, p. 248-250. [q3.] 3. "Note on the magnitude of the difference between successive primes," London Math. So., Jn., v. 9, 1934, p. 276-278. [ft, 278.] 4. Tables of products of small primes. Manuscript in possession of the author. [et.] 0. WESTERN, see BICKMORE and O. WESTERN 1. E. E. WHITFORD. 1. The Pell Equation (Diss. Columbia), New York, 1912, 193 p. [ji, 102- 112: m, 164-190.]* Libraries: CU, DLC, ICU, IU, InU, MdBJ, MB, MCM, MH, MiU, NN, NNC, PEL, PU, RPB, WU 2. "Some solutions of the Pellian equation a:2 — Ay*= ±4," Annals of Math., s. 2, v. 15, p. 157-160, 1913-14. [ji, 158-160.] A. WlEFERICH. 1. "Zur Darstellung der Zahlen als Summen von 51"" und 7**n Potenzen positiver ganzer Zahlen," Math. Ann., v. 67,1909, p8 61-75. [qs*, 74-75.] B. M. WILSON, see SHAH and WILSON. F. WOEPCKE. 1. "Sopra la teorica dei numeri congrui," Annali d. Math., s. 1, v. 3, 1860, p. 206-215. [J3, 214-215.] 2. "Recherches sur plusieurs ouvrages de L6onard de Pise decouverts et publies par M. Le prince Balthasar Boncompagni et sur les rapports qui existent entre ces ouvrages et les travaux mathe'matiques des arabes," Accad. Pontif. d. Nuovi Lincei, Rome, Atti, v. 14, 1860-1, p. 211-227, 241-269. [J3, 266-267.] C. WOLFE. 1. "Ontheindeterminatecubicequationa;'+.Dy'+DV — 3Dxyz= 1,"Calif., Univ., Publ. in Math., v. 1, no. 16, p. 359-369, 1923. [1.] [124]

BIBLIOGRAPHY Woo-Zuc H. J. WOODALL. [See also CUNNINGHAM and WOODALL, CUNNINGHAM, WOODALL and CREAK.] 1. "Mersenne's numbers," Manchester Lit. and Phil. So., Memoirs and Proc., v. 56, 1911-12, no. 1, 5 p. [e2, 2, 3, 5.] H. N. WRIGHT. 1. "On a tabulation of reduced binary quadratic forms of a negative de- terminant," Calif., Univ., Publ. in Math., v. 1, no. 5, 1914, p. 97-114 +app. [n, app.] K. C. YANG. 1. Various generalizations of Waring's problem (Diss. Chicago),Chicago, 1928, iii+43 p. Manuscript. [qa.] Libraries: ICU L. ZAPOLSKAIA [ = SAPOLSKY]. 1. Ueber die Theorie der relativ-abel'schen-cubischen Zahlkorper (Diss. Got- tingen), Gottingen, 1902, vii+481+vi p.+35 plates, [p.] Libraries: CU, CoU, ICJ, ICU, IU, NN, NNC, OCU, PU, RPB A. R. ZORNOW. [See also JACOBI 3.] 1. "De compositione numerorum e cubis integris positivis," Jn. f. d. reine «. angew. Math., v. 14, 1835, p. 276-280. [q,, 279-280.] H. S. ZUCKERMAN. 1. A Universal Waring's theorem for thirteenth powers (Master's thesis Chicago), Chicago, 1934, ii+20 p. Manuscript. [q3.] Libraries: ICU [125]