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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Hensel, K.      218
Hering      225
Hermite, C.      286 287 316 317 323 327
Herschfeld, A.      197
Heuristic arguments      17 87 167
Hilbert symbol      169
Hilbert's 10th problem      69
Hilbert's 7th problem      288 321—322
Hilbert, D.      285 286
History of the Theory of Numbers      178 190
Hjornaes, M.M.      280
Hofmann, J.E.      177
Hoggatt, V.E.      2 307
Honda, T.      166
Hooley, C.      16
Hua, L.K.      155 156
Humbert, P.      166
Hurwitz, A.      293 294 296 297 316
Hutton      186
Hutton, C.      185
Hyyroe, S.      178 189 191 193 194 198—200 204 235
Ideals, classes of      102 103 154
Ideals, conjugates of      150
Ideals, fractional      149 150 152 153
Ideals, invertible      151
Ideals, norms of      159
Ideals, positively oriented bases for      153
Ideals, prime      97—101 105—107
Ideals, primitive      103
Ideals, primitive normalized      103
Ideals, principal      102 105—107 150
Ideals, strict equivalence of invertible      151
Ideals, units of      101 103—105 107 150
Imaginary quadratic field      69 95 195 359
Infinitely many primes      16 17 23 65 66 73 93 193 222 224 226 349 352
Inkeri, K.      33 34 178 189 193—195 198 204
Integral basis      96 104
Irrational numbers, real quadratic      290 291
Irrationality of       307
Irrationality of $\gamma$       282 288
Irrationality of $\pi$       286 288 306
Irrationality of $\sqrt2$       273 286
Irrationality of $\sqrt2^{\sqrt2}$       288
Irrationality of $\zeta(2)$       308
Irrationality of $\zeta(3)$       288 308
Irrationality of e      286 288 302
Irrationality of log r      307
Irrationality of trigonometric functions      307
Irrationality, measure of      299—300 309 310
Irrationalzahlen      303
Irregularity index      145
Isobaric      9
Ivic, A.      231 232
Iwaniec, H.      84
Jacobi series      61
Jacobi symbol      135
Jacobi theta series      58 61
Jacobi, C.G.J.      59 215
Jarden, D.      2 14 15 28
Jobling, P.      72
Johnson, W.      216
Jones, J.P.      69
Jongmans, F.      178
Kahada, Y.      187
Kakeya, S.      51 54
Kanold, H.-J.      19 225
Kaprekar's algorithm      355
Katayama, K.      280
Kaufmann-Buehler, W.      114
Keller, W.      27 28 93 215
Khintchine, A.J.      287 316 331
Kisilevsky, H.      165
Kiss, P.      14
Klein      146 168
Knayswick, D.      25
Knuth, D.      316
Ko, C.      31 178 189 190
Koksma, J.F.      298 321 329 331
Kotov, S.V.      29
Kraetzel, E.      231
Kraus, A.      242
Kronecker symbol      154
Kronecker, L.      271
Kruyswijk, D.      248
Kummer, E.E.      220 347 358
Kunowski, S.      71
L-series      156 158—160 162 164
Lachaud, G.      162 163
Lagarias, J.C.      15 33
Lagrange, J.L.      113—115 132 146 151 176 188 189 200 272 289 290 301
Lambert series      58
Lambert, J.H.      278 285 287 305 306
Landau, E.      51 57 158 204 214 260 284
Landau’s conjecture      see Conjectures Landau's
Lander, L.J.      239 240
Lang, S.      323 325 327 331
Langevin, M.      34 178 202 263
Largest square factor      21
Largest square-free factor      24
Laxton, R.R.      16
Le Lionnais, F.      213 358
Lebesgue, V.A.      178 181 191
Legendre quotient      220
Legendre symbol      13 98 115 154 220
Legendre, A.M.      113—115 135 146 180 285 290 305
Lehmer sequence      5
Lehmer, D.H.      1 4 107 108 204 215
Leibniz, G.W.      184 285
Lekkerkerker, C.G.      18
Lemniscate      115
Lenstra, H.W.      162 166
Leonardo Pisano      1
Lerch, M.      217 219 220 280
Les Grands Courants de la Pensee Mathematique      214 359
Les Nombres Remarquables      215 359
LeVeque, W.J.      85 181 196—198 329
Levinson, N.      74
Li(x)      74
Liber Abaci      2
Lifchitz, H.      75
Lindemann, F.      286 287 316 317 323 324
Linear recurrence sequences      5 6 27
Linfoot, E.H.      107 159
Linnik, Ju.V.      84 160 351
Liouville numbers      286 311 312 316 317 330—332
Liouville, J.      285 295 299 310
Lipman, J.N.      331
Little Book of Big Primes, The      29
Littlewood, J.E.      73
Ljunggren, W.      31 33 182
Llorente, P.      166
Loeh, G.      67 93
Logarithms      20 26 30 34 35 67 70 109 161 179 202 203 217 246 288 322 324 327 346
London, N.      33
Lou, S.      75
Lucas numbers      3 4 8 11 12 16 18 28 30—34 42 43 224 225 263 308
Lucas sequences      2—6 8 9 11 12 15—18 20 21 24 26—29 31 33 36 37 42 43 72 263
Lucas sequences, companion      15 16
Lucas sequences, cubes in      34
Lucas sequences, degenerate      6
Lucas sequences, divisibility properties of      10—11
Lucas sequences, even numbers in      12
Lucas sequences, families of      37
Lucas sequences, powerful numbers in      29—43
Lucas sequences, powers in      29—43
Lucas sequences, prime divisors of      11—27
Lucas sequences, primes in      27—29
Lucas sequences, primitive factors of      18—27
Lucas sequences, quadratic relations in      9
Lucas sequences, square-classes of      30 32

Lucas sequences, square-equivalent      30
Lucas sequences, terms of the form k in      33
Lucas test      72
Lucas, E.      1 10 13 24 72 222 223 225
Ludolph number      185
Lueneburg, H.      19 225
Lueroth, J.      303
Machin, J.      186
Mahler's classification of complex numbers      329—332
Mahler's conjecture      see Conjectures Mahler's
Mahler, K.      6 26 198 233 287 309 315 328—331 345
Maillet, E.      311 331
Makowski, A.      191 235
Malurkar, S.L.      280
Markoff numbers      297—299
Markoff, A.      296 297
Mascheroni's constant      282 283
Masley, J.M.      347
Mason, R.C.      258
Masser's conjecture      see Conjectures ABC
Masser, D.W.      41 42 226 258
Matijasevic, Yu.V.      68 69
Matrices, computing powers of      8
McDaniel, W.L.      36 38—40 233
Meissel, D.F.F.      73
Meissner, W.      214
Melanges Mathematiques, XV      179
Melzak, Z.A.      280
Merel, L.      242
Mersenne numbers      72 87 224 250 252 253 347 354
Mersenne numbers, composite      73 347
Mersenne, M.      225
Mersenne, primes      29 72 73 226
Mertens, F.      282
Method of infinite descent      178 181 189
Metius, A.      183 291
Mignotte, M.      30 85 309 331
Miller's algorithm      71
Miller, G.L.      69 88
Minkowski, H.      331
Mirimanoff, D.      189 216 221
Moebius function      67
Mollin, R.A.      161 163 164 166 232—234 262
Monagan, M.B.      221
Monte Carlo methods      87 88
Montgomery, H.L.      347
Morain, F.      27 71
Moran, A.      67 93
Mordell's conjecture      see Conjectures Mordell's
Mordell, L.J.      42 108 159 262
Nagell, T.      31 33 166 178 180—182 189 190
Nesterenko, Yu.V.      327
New Book of Prime Number Records, The      93
Newton, I.      113 184
Nitaj, A.      235 265
Niven, I.      287 296 305 306 316 331
Non-Euclidean geometry      115 159
Novy, L.      272
Number field      5 239 319 348
Numerus idonei      347 357—359
Nyman, B.      75
Oblath, R.      178 189 191
Odoni, R.W.K.      232
Oesterle, J.      41 157 160 226 258
Olbers, W.      194
Olds, C.D.      287
Order of a quadratic field      149
Ostrowski, A.      204
Oxford English Dictionary      345
p-rank      144 145 166 168 169
Parkin, T.R.      239 240
Pell numbers      4 31—34 43
Pell, J.      189
Penguin Dictionary of Curious and Interesting Numbers, The      359
Pepin, T.      71 223
Perron, O.      287 296 297 302 311 331
Pethoe, A.      29—31 33
Pi and the AGM      188
Pigeon-hole principle      286 297
Pillai, S.S.      197
Plouffe, S.      187
Pocklington, H.C.      83 84 86 89
Pollaczek, F.      221
Polynomial algorithm      70
Polynomial function      70
Polynomial time      86 87 89
Polynomials, cyclotomic      24 195
Polynomials, homogeneous      116 244 313
Polynomials, homogenized cyclotomic      24
Polynomials, irreducible      237 265 274 276 313
Polynomials, minimal      274 300 301
Polynomials, monic      148 274
Polynomials, optimal prime producing      350 351
Polynomials, powers as values of      246
Pomerance, C.      70 87 215 217 225 351
Popken, J.      317 321 330
Powell, B.      241 247 248 254
Powerful numbers      230—236
Powerful numbers, consecutive      235 236 255 258
Powerful numbers, distribution of      231—233
Powerful part of an integer      43
Primality tests      2
Primality-testing algorithms      70
Primary representations      155
Prime certificate      29
Prime number tests      72
Prime number theorem      17 25 74—76 81
Prime numbers, distribution of      80
Prime numbers, formulas for nth      67—68
Prime numbers, gaps between      75 76
Prime numbers, inert      97 98 100 103 105—108 110
Prime numbers, large      72 76 83 143
Prime numbers, largest      see Records largest
Prime numbers, primorial of      349
Prime numbers, probable      28
Prime numbers, producing      89
Prime numbers, ramified      103
Prime numbers, small      76 85 89
Prime numbers, Sophie Germain      224
Prime numbers, twin      76 224 348 349 351 359
PRIMES      see Prime numbers
Primitive factor      18—21 25 42 250
Primitive representations      103 105–107 117 119 121–123 134—136 155
Primorial      see Prime numbers primorial
Principia      114
Pritchard, P.A.      67 93
Probabilistic algorithms      70
Probabilistic prime number test      71
Proper powers      17 23 29 177 192 194
Pseudoprimes      71 88—89
Puccioni, S.      221 249
Pythagoras      272 285
Pythagorean triples      236—238
quadratic characters      138
Quadratic field      69 95 103 148 149 155 165 166 195 220 240 359
Quadratic fields, imaginary      69 92 95 102 108—110 158 161 164 166 167 195 350 351
Quadratic fields, real      106 162—165 167 350
Quadratic reciprocity law      115 140
Quadratics      165
Quartic equations      37 40 240
Quer, J.      165 166
Rabin's test      71 89
Rabin, M.O.      70 88
Rabinovitch, G.      68 108 349
Radical      227 259 262 264 266
Radoux, C.      350
Ram Murty, P.M.      260
Ramachandra, K.      325 331
Ramanujan's Notebooks      280
Ramanujan, S.      279 352

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