Ribenboim P. — My numbers, my friends: popular lectures on number theory :: Электронная библиотека попечительского совета мехмата МГУ

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Ribenboim P. — My numbers, my friends: popular lectures on number theory

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Название: My numbers, my friends: popular lectures on number theory

Автор: Ribenboim P.

Аннотация:

This is a selection of expository essays by Paulo Ribenboim, the author of such popular titles as "The New Book of Prime Number Records" and "The Little Book of Big Primes". The book contains essays on Fibonacci numbers, prime numbers, Bernoulli numbers, and historical presentations of the main problems pertaining to elementary number theory, such as for instance Kummer's work on Fermat's Last Theorem. The essays are written in a light and humorous language without secrets and are thoroughly accessible to everyone with an interest in numbers.

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Рубрика: Математика/Теория чисел/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 384

Добавлена в каталог: 08.06.2005

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Предметный указатель

$\pi$ , continued fraction expansion of      279
$\pi$ , digits of      63 185 187 188
$\pi$ , expressions for      184—187 278 279 283
$\pi(x)$       16 17 73 74 81
13 Lectures on Fermat’s Last Theorem      238
17-gon      115
Aaltonen, M.      195
Abel, N.H.      215 272 275
Absolutely convergent      59 75
Adleman, L.M.      70 237 257
Agoh, T.      283
Algebraic independence      61 288 318 328
Algebraic integers      7 69 95 96 110 148 149 274 276 312 314 319 359
Alladi, K.      299 308
Almqvist      60
Alternating groups      276 353 354
Ambiguous classes      138 144 145 167
Andre-Jeannin, R.      40 60 307
Ankeny, N.C.      166
Apery, R.      60 280 287 307 308
Aphrodite      82
Apollo      82
Approximation by rational numbers      296—302
Archimedes      183 291
Arctangent      185
Arima, R.      291
Arithmetic progressions      94
Arithmetic-geometric mean      115 188
Ars Conjectandi      114
Artin's conjecture      see Conjectures Artin's
Artin's constant      84
Artin, E.      16 19 225
Asymptotic density      25 27 242
Ayoub, R.G.      108
Bachmann, P.      180
Bailey, D.H.      187
Baillie, R.      70
Baker, A.      19 25 29 34 68 108 160 178 201 245 287 308 321 323 324 327 331 345 349 350 358
Balasubramanian, R.      347
Bang, A.S.      1 17 19 195 225 248
Bateman, P.T.      230 231
Becker, P.G.      307
Beeger, N.G.W.H.      215
Ben Gerson, L.      177 178
Berndt, B.C.      279 280
Bernoulli numbers      197 219 222 280 281
Bernoulli, J.      113
Bertrand, J.      75 79
Beukers, F.      241 243 307 309
Binary linear recurrence      15 17
Binet's formulas      6 8
Binet, J.P.M.      5 55
Birkhoff, G.D.      19 23 195 225
Bit operations      86
Bombelli, R.      287
Bombieri, E.      84
Bond, R.      34
Book of Prime Number Records, The      64
Borel, E.      330
Borevich, Z.I.      155
Borwein, J.M.      187
Bouniakowsky, A.      92 236 237
Bourbaki group      214
Bouyer, M.      186
Boyd, D.W.      165
Brauer, A.A.      15
Bray, H.      192 257
Brazil      29 113
Brent, R.P.      71 75 290
Briggs, W.E.      161 357
Brillhart, J.      21 28
Brouncker, W.      184 278
Brown, J.L.      53
Brun's constant      76
Brun, V.      75 348
Buell, D.A.      157 166
Bugeaud, Y.      34
Bukhadze, E.A.      309
Bundschuh, P.      271 315 330
Burrowes, R.      72
Caldwell, C.      64
Cantor, G.      275 286 302 309
Cardano, G.      272
Carlitz, L.      60
Carmichael function      14
Carmichael, R.D.      1 10 13 17—19 24 27 191 225
Cassels, J.W.S.      178 190 191 197 331
Castellanos, D.      278
Catalan's Conjecture      32 34 35 251
Catalan, E.      34 177 178 191
Catalan’s conjecture      see Conjectures Catalan's
Characteristic polynomial      3 14
Chebyshev's theorem      55
Chebyshev, P.L.      73 75 79 80 88
Chein, E.Z.      31 189 190
Chevalley, C.      353
Chord and tangent method      39
Chowla, S.      108 161 163 166 357
Chudnovsky, D.V.      309
Chudnovsky, G.V.      309
Clark, D.      215
Clarkson, R.      71
Class group      163 166—169
Class number      69 92 102—111 113 138 151 152 156 157 159 161—165 167—169 195 196 203 204 220 348 350 351 359
Class number and the relationship between strict class number      152
Class number formula      154—158
Class number, calculation of      104—106
Class number, strict      151 152 157
Clausen, T.      186
Coates, J.      345
Cohen, H.      162 166
Cohn, J.H.E.      30 31 36 38 39 41 235
Complex plane      75
Computers      32 34 35 72 82 86 176 187 216 226 240
Comtet, L.      280
Conductor of an order      149
Conjectures, ABC      42 43 227 259—266
Conjectures, Artin's      17
Conjectures, Catalan's      35 178 260
Conjectures, Goldbach's      77
Conjectures, Landau's      261
Conjectures, Mahler's      330
Conjectures, Masser's      see Conjectures ABC
Conjectures, Mordell's      43
Conjectures, Schanuel's      324—328
Conrey, J.B.      74
Consecutive composite numbers      75 76
Consecutive prime values      69
Construction of regular polygons      115
Continued fraction expansions      30 298 302
Continued fraction expansions of $\pi$       292—295
Continued fraction expansions of e      292—295
Continued fractions      288—295
Convenient numbers      142 143 357 358
Cox, D.A.      168
Craig, M.      165
Crandall, R.E.      71 215 217
Crelle's Journal      178 216 276
Crelle, A.L.      177
Criterion of Pocklington      83
Critical line      75
Cubic diophantine equations      34
Cyclotomic polynomials      see Polynomials cyclotomic
Dahse, Z.      186
Darmon, H.      240 242
Davenport, H.      198 347
De Bessy, F.      177 183 189
de La Vallee Poussin, C.      73 80
De Lagny, F.      186
De Leon, M.J.      254

De Vitry, F.      177
Dedekind $\zeta$ function      17
Dedekind, R.      146 150
Degenerate binary recurrence      30
Degenerate sequences      7
Deleglise, M.      73
Deshouillers, J.-M.      347
Deterministic algorithms      70
Deterministic tests      87
Deuring, M.      108 159 160
di Pisa, L.      183
Dickson, L.E.      177 189 225 353
Dilcher, K.      215 217
Diophantine approximation      179 199 286—288 313
Diophantus of Alexandria      190
Dirichlet, G.L.      84 92 135 146 153 219 236 281 285 295 296
Discriminants      3 25 40 43 96 102 106 108 117—119 121—132 134—139 141—149 152—155 157—167 169 263 284
Discriminants of an order      149
Discriminants, calibers of      163 164
Discriminants, fundamental      118 119 125—127 129 131 132 138 141—144 146 148 149 152 153 157—159 162—164 167
Disquisitiones Arithmeticae      102 115 116 145—147 195 345
Distinct prime factors      17 21 24 25 67 107 167 202 227
Double-squares      31 32 36
Dress, F.      347
Dubner, H.      27 28 76
Durand, A.      330
Durst, L.K.      18
Dvornicich, R.      309
Dyadic representation      55
Dyson, F.J.      314
D’Alembert      273
Edwards, H.M.      115
Effective minoration      161
Effectively computable      20 21 26 27 30 31 33 35 40 41 161 206 233 246 251 260 315
Eisenstein, F.G.      192 216 223 246 274
Eisenstein,F.G.      115
Elements      65
Elkies, W.D.      41 239 240 260
Elliptic curve      39 243
Elliptic functions      58 109 161
Engel, F.      303
Eratosthenes      81
Erdoes, P.      24 204 229—232 234 235 254 311
Error terms      74 75
Euclid      64 348
Euler, L.      10 13 23 54 64 65 68 72 113—115 140—142 146 177 179—181 184—186 189 191—193 218 222 223 239 276 277 281 282 285 287 289 292 293 301 320 348 349 351 356 357
Exponential-diophantine equation      201 202
Extended Richaud — Degert type      164 165
Fadiman, C.      213
Faltings, G.      42 238
Fel’dman, N.I.      331
Ferentinou-Nicolacopoulou, J.      191 193
Fermat numbers      66 72 87 192 193 250 252—254 258 262 276
Fermat numbers, square-free      193
Fermat primes      29 224 276
Fermat's last theorem      43 67 193 221 226 236 238 240 241 247 258—261 287 309 348 352 359
Fermat's Last Theorem for Amateurs      250
Fermat, P.      114 132 134 146 177 182 183 189 191 192 222 223 247 290
Fermat’s Little Theorem      14 71 72 84 88 215 217 223 247
fibonacci      1 183 223
Fibonacci numbers      2 4 13—15 31—34 42 348 360
Fibonacci numbers, cubes      34
Fibonacci numbers, square-classes of      32
Fibonacci numbers, squares      31
Fibonacci Quarterly      8
Fibonacci sequence      56
Finite abelian group      138 144 166
Finite fields      6
Finkelstein, R.      33
Fischer, B.      353
Flath, D.E.      143
Forms reduction      125
Forms, automorphs of      123 132—135
Forms, binary quadratic      102 113 115—119 136 144 358
Forms, conjugates of      118
Forms, indefinite      117 127 129 146
Forms, linear      20 26 30 34 35 109 161 179 202 203 246 322 324 346
Forms, negative definite      118
Forms, positive definite      118 123 124 129 158
Forms, primary representations of      155
Forms, primitive      117 118 120 121 132 136—138 141 143 147 152—155 163
Forms, primitive values of      117
Forms, principal      117 137
Forms, reduced      123—132 134 138 142 163 164
Forms, special reduced      123
Forms, values of      117
Fourier, J.      285 301
Fouvry, E.      237 257
Franklin, P.      178
Frei, G.      142 358
Fridy, J.A.      53
Friedlander, J.B.      84 163
Friedmann, A.      218 220
Frobenius, F.G.      221 349
Fundamental theorem of algebra      115 274
Fundamental units of a ring      101 152 155 157 162 163 182 183 191 349
Furtwaengler, P.      221
Gallot, Y.      72
Galois group      276 284
Galois, E.      272 275 290
Gamma function      282
Gandhi's formula      67
Gandhi, J.M.      66
Gauss sum      195
Gauss' reciprocity law      111 154
Gauss, C.F.      72 73 80 101 106 108 114 176 186 187 194 272—274 344 346 357
Gel’fond, A.O.      160 287 320 321 323—325 331
Generalized Euler function      14
Genus, principal      140—143 145—147 162 169
Gerono, G.C.      34 190
GIMPS (Great Internet Mersenne Prime Search)      72
Glaisher, J.W.L.      278 282
Goldbach's conjecture      see Conjectures Goldbach's
Goldbach, C.      65 281
Goldberg, K.      217
Golden number      163
Golden ratio      see Golden number
Goldfeld, D.M.      108 157 159 160
Goldman, M.      32
Golomb, S.W.      229 230
Good, I.J.      307
Gramain, F.      327
Granville, A.      221 237 238 240 248 257 259 265
Grave, D.      187 188
Gray, J.J.      114
Greatest prime factor      24 25 199
Gregory, J.      184 277
Gross, B.      108 160 239
Grosswald, E.      161 231 280 357
Growth of coefficients of Taylor series      7
Grube, F.      357
Guilloud, J.      186
Guinness Book of Records, The      63 188
Gut, M.      194
Guy, R.K.      359
Gyoery, K.      19
Hadamard, J.      73 80
Halberstam, H.      318
Hall      262
Hampel, R.      191 195 196
Hardy, G.H.      24 59 65 66 281 282
Hasse, H.      15
Hata, M.      309
Heath, T.L.      189
Heath-Brown, D.R.      84 232 237 238 257 351
Hebracus, L.      177
Hecke, E.      108 158
Heegner, K.      68 108 159 160 349 358
Heilbronn, H.      107 108 159 161
Hendy, M.D.      349

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