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From page 173... ... T 76, 87 Bernoulli numbers 10, 36, 50 polynomials 10 Bertelsen 40 Berwick 21, 72, 87 Bickmore 30, 55, 60, 66, 77, 87, 127, 128, 167 Biddle 51, 87 Bilevich 76, 96 Billing 64, 88 Binary cubic forms 72 quadratic forms 8, 48, 53-60, 68-74 scale of notation 12, 37 Binomial coefficients 11, 36 congruence 7, 12-24, 37 equation 28, 69, 72-74 Bisconcini 62, 88 Borisov 71, 88, 128 Bork 15, 88, 128 Brahmagupta 58 Bretschneider 61, 82, 88, 128, 168 British Ass. Read the entire page →
From page 174... ... L 6-10, 12, 16, 25, 33, 4(M4, 68, 69, 76, 101-103, 131, 139, 142, 169 Goldbach's Problem 79-80 Goldberg 14, 26, 103, 142-145 Goldschmidt 41 Golubev 27, 103 Goodwyn 8, 12, 16, 103 Cosset 23, 94, 103 Gouwens 74, 103, 145 Gram, 9, 40, 43, 103 Grave 13, 18, 26, 74, 80, 104, 146 Gupta 78, 79, 82, 83, 104 Haberzetle 83, 104 Hadlock 71, 104 Hall 10, 35, 104 Halsted 61, 62, 104, 146, 169 Hardy 43, 45, 78, 79, 82, 104, 105, 146 Haussner 10, 16, 80, 105, 147-149 Heaslet 18, 123 Henderson 24 Hertzer 15, 105, 128, 149 Hessian 71 Highly composite numbers 8 Holden 74, 105 Hollerith cards 48, 50 Hoppenot 21, 27, 33, 39, 42, 44, 105, 108 Houel 12, 18, 105, 109 Husquin 41, 42, 106 Ideals 67, 75 Idoneals 46, 48, 60, 70 Indeterminate equations 49-50, 54-66 Index 12, 17-20, 75, 76 Index of perfection 5 Ince 56, 57, 67, 75, 106 Inghirami 26, 106, 150, 151 Inverse totient 6 Inversion function M (n) Read the entire page →
From page 175... ... T 10,52,82,110, 111 Lenhart64, 111 Levanen 19, 54, 111, 161 Levy 120 Lidonne 26, 111 Linear congruences 49, 50 Diophantine equations 49, 50 divisors 53, 54 forms 47, 49, 50, 53, 54 Littlewood 43, 82, 104 Lodge 24, 25, 37, 48, 113, 115, 133, 141 Logarithms 37 Logarithmic integrals 40, 45 Lucas 6, 10, 17, 29, 33, 35, 54, 74, 112, 161 Lucas' functions 28, 35 MacMahon 78, 112 Markov 71, 112 Martin 61, 62, 112, 146, 169 Maser 100, 110 Mason 5, 6, 89, 112 Massarini 91 Mathews 48, 70, 72, 74, 112 Maties 22, 113 Mauch 82, 113 Mechanical computing 13, 48-51, 57 Meissel 40 Meissner 10, 16, 21, 113, 127 Merrifield43,113,162 Mersenne numbers 28, 29 Mertens 7, 9, 113 Miller 6, 37, 113, 135, 136, 152 Mitchell 169 Mitra24, 113 Mobius inversion function 7, 9, 10, 28, 72 Modular functions 71, 78 Moreau 7, 113 Moritz 10, 113 Multiply amicable numbers 5, 8 perfect numbers 5, 8 Nagell 56, 113 Nielsen 56, 58, 59, 67, 114 Niewiadomski 22, 114 Norm 28, 35, 75, 76 Numbers, abundant 5 8 algebraic 75-77 amicable 5, 8 Bernoulli 10, 36, 50 Fermat 28, 59, 72 figurate 11 highly composite 8 Mersenne 28, 29 multiply amicable 5, 8 multiply perfect 5, 8 perfect 5 polygonal 83 sociable 6 triangular 11 Number of divisors 8, 9 Numerical functions 6-11 25 Oettinger 58, 64, 65, 114 Ostrogradsky 13, 18, 114, 162 Pagliero 39,114,162 Pall 71, 107 Paradine 62, 114 Partial fractions 11 Partitions 77-79 Partitions, quadratic 23, 44, 45, 59, 60, 79 Pell equation 32, 35, 54-59, 66, 67 Perfect numbers 5 Periodic decimals 11, 12, 15, 30 Perott, 7, 114 Perron 55, 67, 114, 115 Peters 24, 25, 36, 48, 115, 133, 141 Petzval 109 Pillai 82, 115 Pierce 35 Pipping 80, 115,149 Pocklington 74, 115 Poletti 26, 38-40, 43, 44, 46, 47, 115, 116, 162 Polygon, regular 72 Polygonal numbers 83 Polynomials, Bernoulli 10 cyclotomic 28, 69, 72-74 [175] Read the entire page →
From page 176... ... INDEX Posse 14, 19, 116 Poulet 5, 6, 10, 24, 35, 48, 116, 117, 139, 162, 163 Poullet-Delisle 100 Power residue 12, 13, 22, 23 Powers of a primitive root 17-19, 75, 76 Primality tests 48 Prime pairs 42-44 Primes, distribution of 40-43, 46 identification of 48 lists of 37-39 of special form 43-47 Primitive root 11-19, 22, 52, 76 Quadratic characters 17, 47, 48, 51-54 congruences 50-54, 66 Diophantine equations 54-62, 66 fields 57, 69, 75, 76 forms 8, 48, 53-60, 68-74 partitions 23, 44, 45, 59, 60, 79 residues 43, 44, 47, 48, 52, 53, 59 Quartic Diophantine equations 65 fields 76, 77 forms 65 Quaternary quadratic forms 72 Ramanujan 8, 78, 79, 105, 117, 146, 163 Rank of apparition 17 Reciprocity, Law of 52 Recurring series 10, 17, 35, 36, 56, 61 Reid 76, 117 Residue, higher 12, 13, 22, 23, 59 quadratic 43, 44, 47, 48, 52, 53, 59 Residue-index 11, 13, 15-17, 23 Reuschle 13-16, 20, 23, 29, 30, 32, 59, 62, 72, 73, 77,117,163-167 Richmond 65, 117 Riemann 40, 41 Riemann hypothesis 9 Roberts 67, 117, 118, 167 Robinson 50, 118 Rosenberg 95 Ross 70-72, 118 Sang 61, 62, 118, 167 Saorgio 61, 118 Sapolsky see Zapolskafa Sarma7, 118, 167 Schady 52, 118 Schaffstein 75, 118 Schapira 91 Scherk44, 80, 118 Schulze61,118, 168 Seeber 71, 118 Seelhoff 48, 70, 119 Seeling 56, 66, 67, 119 Selling 71, 72 Shah 80, 119 Shanks 15, 30, 119, 128,168 Shook 82, 119 Sieve process 26, 27, 31, 46 Simerka62, 119 Simony 37, 119 Sociable numbers 6, 8 Sominskil 76, 96 Sommer 75, 120, 169 Sparks 82, 120 Square endings 48, 52 Stackel 43, 80, 120 Stager 25, 40,120 Stein 36, 115 StencUs 26, 27, 47, 48, 50, 53 Sterneck 7, 9, 81, 120, 121, 169 Stieltjes 22, 121 Struve 59 Sturani 38, 39, 46, 116 Suchanek 37, 121 Sugar 82, 121 Sum of divisors 5, 8, 9 of products of consecutive integers 10 of powers 10 Suryanarayana 70, 121 Sutton 43, 121 Sylvester 6, 7, 72, 73, 121, 169 Symmetric functions 10, 77 Tait 79, 122 Tanner 60, 73, 77, 122, 167, 169 Tchebychef see Chebyshev Tebay 61, 62, 122, 169 Teege 74, 122, 170 Ternary quadratic forms 71, 72 Ternouth 24, 25, 48, 115, 133, 141 Terry 52, 122 Thebault 52, 122 von Thielmann 67, 122 Totient 6, 7, 13, 16, 20, 28, 73 Townes 72, 122 Travers 5, 122 Triangular numbers 11 Triangles, rational 60-62 right 60-62 Tschebyschew see Chebyshev Twin primes 42-44 Umeda 79, 122 Units 57, 75, 76 Uspensky 18, 123 Valroff 22, 123 Vandiver 36, 123, 151 Vega 26, 38, 123, 170 Verebrfusov 65, 123, 170 Voronol 76, 123 Waring's problem 81-83 [176 Read the entire page →
From page 177... ... INDEX Watson 79, 123 Woepcke 62, 124 Weinreich 80,123 Wolfe 64, 124 Werebrusow see Verebrflsov Woodall 14-16, 22, 23, 27-31, 36, 38, 39, 47, Wertheim 14, 18, 49, 52, 54, 55, 123, 124, 163, 94-95, 125, 134-137, 145, 154-156 170 Wright 70, 125 Western, A Read the entire page →

From page 173...

... T 76, 87 Bernoulli numbers 10, 36, 50 polynomials 10 Bertelsen 40 Berwick 21, 72, 87 Bickmore 30, 55, 60, 66, 77, 87, 127, 128, 167 Biddle 51, 87 Bilevich 76, 96 Billing 64, 88 Binary cubic forms 72 quadratic forms 8, 48, 53-60, 68-74 scale of notation 12, 37 Binomial coefficients 11, 36 congruence 7, 12-24, 37 equation 28, 69, 72-74 Bisconcini 62, 88 Borisov 71, 88, 128 Bork 15, 88, 128 Brahmagupta 58 Bretschneider 61, 82, 88, 128, 168 British Ass.

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From page 174...

... L 6-10, 12, 16, 25, 33, 4(M4, 68, 69, 76, 101-103, 131, 139, 142, 169 Goldbach's Problem 79-80 Goldberg 14, 26, 103, 142-145 Goldschmidt 41 Golubev 27, 103 Goodwyn 8, 12, 16, 103 Cosset 23, 94, 103 Gouwens 74, 103, 145 Gram, 9, 40, 43, 103 Grave 13, 18, 26, 74, 80, 104, 146 Gupta 78, 79, 82, 83, 104 Haberzetle 83, 104 Hadlock 71, 104 Hall 10, 35, 104 Halsted 61, 62, 104, 146, 169 Hardy 43, 45, 78, 79, 82, 104, 105, 146 Haussner 10, 16, 80, 105, 147-149 Heaslet 18, 123 Henderson 24 Hertzer 15, 105, 128, 149 Hessian 71 Highly composite numbers 8 Holden 74, 105 Hollerith cards 48, 50 Hoppenot 21, 27, 33, 39, 42, 44, 105, 108 Houel 12, 18, 105, 109 Husquin 41, 42, 106 Ideals 67, 75 Idoneals 46, 48, 60, 70 Indeterminate equations 49-50, 54-66 Index 12, 17-20, 75, 76 Index of perfection 5 Ince 56, 57, 67, 75, 106 Inghirami 26, 106, 150, 151 Inverse totient 6 Inversion function M (n)

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From page 175...

... T 10,52,82,110, 111 Lenhart64, 111 Levanen 19, 54, 111, 161 Levy 120 Lidonne 26, 111 Linear congruences 49, 50 Diophantine equations 49, 50 divisors 53, 54 forms 47, 49, 50, 53, 54 Littlewood 43, 82, 104 Lodge 24, 25, 37, 48, 113, 115, 133, 141 Logarithms 37 Logarithmic integrals 40, 45 Lucas 6, 10, 17, 29, 33, 35, 54, 74, 112, 161 Lucas' functions 28, 35 MacMahon 78, 112 Markov 71, 112 Martin 61, 62, 112, 146, 169 Maser 100, 110 Mason 5, 6, 89, 112 Massarini 91 Mathews 48, 70, 72, 74, 112 Maties 22, 113 Mauch 82, 113 Mechanical computing 13, 48-51, 57 Meissel 40 Meissner 10, 16, 21, 113, 127 Merrifield43,113,162 Mersenne numbers 28, 29 Mertens 7, 9, 113 Miller 6, 37, 113, 135, 136, 152 Mitchell 169 Mitra24, 113 Mobius inversion function 7, 9, 10, 28, 72 Modular functions 71, 78 Moreau 7, 113 Moritz 10, 113 Multiply amicable numbers 5, 8 perfect numbers 5, 8 Nagell 56, 113 Nielsen 56, 58, 59, 67, 114 Niewiadomski 22, 114 Norm 28, 35, 75, 76 Numbers, abundant 5 8 algebraic 75-77 amicable 5, 8 Bernoulli 10, 36, 50 Fermat 28, 59, 72 figurate 11 highly composite 8 Mersenne 28, 29 multiply amicable 5, 8 multiply perfect 5, 8 perfect 5 polygonal 83 sociable 6 triangular 11 Number of divisors 8, 9 Numerical functions 6-11 25 Oettinger 58, 64, 65, 114 Ostrogradsky 13, 18, 114, 162 Pagliero 39,114,162 Pall 71, 107 Paradine 62, 114 Partial fractions 11 Partitions 77-79 Partitions, quadratic 23, 44, 45, 59, 60, 79 Pell equation 32, 35, 54-59, 66, 67 Perfect numbers 5 Periodic decimals 11, 12, 15, 30 Perott, 7, 114 Perron 55, 67, 114, 115 Peters 24, 25, 36, 48, 115, 133, 141 Petzval 109 Pillai 82, 115 Pierce 35 Pipping 80, 115,149 Pocklington 74, 115 Poletti 26, 38-40, 43, 44, 46, 47, 115, 116, 162 Polygon, regular 72 Polygonal numbers 83 Polynomials, Bernoulli 10 cyclotomic 28, 69, 72-74 [175]

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From page 176...

... INDEX Posse 14, 19, 116 Poulet 5, 6, 10, 24, 35, 48, 116, 117, 139, 162, 163 Poullet-Delisle 100 Power residue 12, 13, 22, 23 Powers of a primitive root 17-19, 75, 76 Primality tests 48 Prime pairs 42-44 Primes, distribution of 40-43, 46 identification of 48 lists of 37-39 of special form 43-47 Primitive root 11-19, 22, 52, 76 Quadratic characters 17, 47, 48, 51-54 congruences 50-54, 66 Diophantine equations 54-62, 66 fields 57, 69, 75, 76 forms 8, 48, 53-60, 68-74 partitions 23, 44, 45, 59, 60, 79 residues 43, 44, 47, 48, 52, 53, 59 Quartic Diophantine equations 65 fields 76, 77 forms 65 Quaternary quadratic forms 72 Ramanujan 8, 78, 79, 105, 117, 146, 163 Rank of apparition 17 Reciprocity, Law of 52 Recurring series 10, 17, 35, 36, 56, 61 Reid 76, 117 Residue, higher 12, 13, 22, 23, 59 quadratic 43, 44, 47, 48, 52, 53, 59 Residue-index 11, 13, 15-17, 23 Reuschle 13-16, 20, 23, 29, 30, 32, 59, 62, 72, 73, 77,117,163-167 Richmond 65, 117 Riemann 40, 41 Riemann hypothesis 9 Roberts 67, 117, 118, 167 Robinson 50, 118 Rosenberg 95 Ross 70-72, 118 Sang 61, 62, 118, 167 Saorgio 61, 118 Sapolsky see Zapolskafa Sarma7, 118, 167 Schady 52, 118 Schaffstein 75, 118 Schapira 91 Scherk44, 80, 118 Schulze61,118, 168 Seeber 71, 118 Seelhoff 48, 70, 119 Seeling 56, 66, 67, 119 Selling 71, 72 Shah 80, 119 Shanks 15, 30, 119, 128,168 Shook 82, 119 Sieve process 26, 27, 31, 46 Simerka62, 119 Simony 37, 119 Sociable numbers 6, 8 Sominskil 76, 96 Sommer 75, 120, 169 Sparks 82, 120 Square endings 48, 52 Stackel 43, 80, 120 Stager 25, 40,120 Stein 36, 115 StencUs 26, 27, 47, 48, 50, 53 Sterneck 7, 9, 81, 120, 121, 169 Stieltjes 22, 121 Struve 59 Sturani 38, 39, 46, 116 Suchanek 37, 121 Sugar 82, 121 Sum of divisors 5, 8, 9 of products of consecutive integers 10 of powers 10 Suryanarayana 70, 121 Sutton 43, 121 Sylvester 6, 7, 72, 73, 121, 169 Symmetric functions 10, 77 Tait 79, 122 Tanner 60, 73, 77, 122, 167, 169 Tchebychef see Chebyshev Tebay 61, 62, 122, 169 Teege 74, 122, 170 Ternary quadratic forms 71, 72 Ternouth 24, 25, 48, 115, 133, 141 Terry 52, 122 Thebault 52, 122 von Thielmann 67, 122 Totient 6, 7, 13, 16, 20, 28, 73 Townes 72, 122 Travers 5, 122 Triangular numbers 11 Triangles, rational 60-62 right 60-62 Tschebyschew see Chebyshev Twin primes 42-44 Umeda 79, 122 Units 57, 75, 76 Uspensky 18, 123 Valroff 22, 123 Vandiver 36, 123, 151 Vega 26, 38, 123, 170 Verebrfusov 65, 123, 170 Voronol 76, 123 Waring's problem 81-83 [176

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From page 177...

... INDEX Watson 79, 123 Woepcke 62, 124 Weinreich 80,123 Wolfe 64, 124 Werebrusow see Verebrflsov Woodall 14-16, 22, 23, 27-31, 36, 38, 39, 47, Wertheim 14, 18, 49, 52, 54, 55, 123, 124, 163, 94-95, 125, 134-137, 145, 154-156 170 Wright 70, 125 Western, A

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INDEX Pages 173-181

INDEX
Pages 173-181