Krizek M., Somer L., Luca F. — 17 Lectures on Fermat Numbers: From Number Theory to Geometry :: Электронная библиотека попечительского совета мехмата МГУ

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Krizek M., Somer L., Luca F. — 17 Lectures on Fermat Numbers: From Number Theory to Geometry

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Название: 17 Lectures on Fermat Numbers: From Number Theory to Geometry

Авторы: Krizek M., Somer L., Luca F.

Аннотация:

The pioneering work of French mathematician Pierre de Fermat has attracted the attention of mathematicians for over 350 years. This book was written in honor of the 400th anniversary of his birth, providing readers with an overview of the many properties of Fermat numbers and demonstrating their applications in areas such as number theory, probability theory, geometry, and signal processing. This book introduces a general mathematical audience to basic mathematical ideas and algebraic methods connected with the Fermat numbers.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2002

Количество страниц: 257

Добавлена в каталог: 11.04.2008

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      xvii 205 207
th root of unity      148
$\check{S}$ ofr, B.      202 203
$\check{S}$ olcov $\acute{a}$ , A.      xvii
Abel, N.H.      35 193
Acoustics      167
Actor, proper prime      77
Address      174
Adleman, L. M.      7 13 47 138
Agarwal, R. C.      167-170
Ahmes series      104 107 113
Aigner, A.      43 44
Akushskii, I. Ya      58
al - Farisi      101
Alford, W.R.      136
Algebra, abstract      188
Algebra, Hecke      xii
Algebraic fraction      56
Algorithm      6 7 49 173 179 186
Algorithm, deterministic polynomial-time      58
Algorithm, division      11 189
Algorithm, Euclidean      11 12 16 72
Algorithm, factoring      7
Algorithm, nondeterministic polynomial      8
Algorithm, parallel      170
Altitude      97 98
Amplitude      167
Analysis, graphical      57
Analysis, spectral      167
Ancient Greeks      3
Andre - Jeannin, R.      115
angle      97 203
Angle, right      100
Antonyuk, P. N.      179 182 184-186
Apollonius      xii xv
applications      ix xiii xvi 3 13 165
Archimedes      x xii
Argument      191
Argument, contradiction      213
Argument, heuristic      3
Argument, heuristic probabilistic      158
Argument, modular      82
Arithmetic, binary      80 165 171 173
Arithmetic, complex      167
Arithmetic, integer      171
Arithmetic, long integer      171
Arithmetic, modular      58 171
Arithmetic, modulo a Fermat number      171
Arithmetic, modulo a Mersenne number      171
Arithmetic, multiprecision      58
Arithmetic, simplified binary      170
Arithmetic, special binary      172
Array      186
Artjuhov, M.M.      70
Arya, S. P.      32
Asadulla, S.      97
Astronomy      x
Asymptotic equality      5
Atkin, A. O. L.      4 5
atom      6
Attractor-curve      185
Automorphism      192
Automorphism, Galois      192
Bachet de M $\acute{e}$ ziriac, C. G.      ix x
Backward substitution      13
Bacon, F.      xiii
Badea, C.      115
Baillie, R.      70 73 210
Baker, A.      73
Balasubramanian, R.      58
Banachiewicz, T.      37
Barner, K.      vii
Barrow, I.      xv
Base      43 56 57 108 135 137 138 141 142 149-154
Basis      188
Beeger, N.G.W.H.      68 131
Beiler, A.H.      80 203
Bellon, M. P.      177
Bennett, G.      38 39
Bernoulli, J.      36
Beukers, F.      80
Bicknell, M.      114
Biermann, K. - R.      3
Bifurcation      182 184
Bifurcation diagram      184
Binary expansion      87
Birkhoff, G.D.      140 148
Bit shift      167 172
Bj $\ddot{o}$ rn, A.      154
Bojanic, R.      101
Bolyai, J.      37
Borwein, P.      116
Bosma, W.      70
Brahmagupta      x
Branch      185
Bray, H. G.      68 217
Brent, R. P.      3-5 7 67 70 158 208 210
Bressoud, D. M.      7
Brillhart, J.      3-5 41 63 70 142 153 208 210 212 214
Bro $\check{z}$ ek, J.      xv
Broscius, J.      xv
Brun, V.      113
Buchmann, J.      154
Buell, D. A.      5 43 73 209
Bugeaud, Y.      152
Burrus, C. S.      167-170
Burton, D.M.      12 18-20 24 25 31 32 38 43 49 50
Burtsev, V. M.      58
Calculus, differential      vii
Calculus, integral      vii
Canals, I.      43
Cardinality      22 51 174 188 192
Carlip, W.      136 137
Carmichael, R. D.      20 119 134 136
Carvalho, J. B.      5
Cauchy, A. L.      x 218
Chabbert, P.      viii
Chang, C. C.      39 174-176
Chang, J. J.      171
Chaos      3 177 179
Chinese calendar      16
Chleboun, J.      40 60 67 70 160
Cipolla, M.      132
circle      193 203
Circle, unit      181 198
Circular arc      205
Cissoid      xiv
Class NP      8
Clausen, T.      3 4 208
Coefficients, binary      172
Coefficients, binomial      80 82 117
Coefficients, integer      182 199 200
Coefficients, rational      182 189 190
Cofactor      46
Cohen, H.      47 138
Compact disk      170
compass      2 3 33-35 85 109 117 187 190-192 194 197 202 205 206
Complex plane      179 190 198
Complexity of arithmetic operations      167
Component      55 56
Compositeness      5 7 43
Computer      3 158
Computer analysis      5
Computer factorization      163
Computer memory      174
Computer testing      3
Conchoid      xiv
Condition, initial      182
Condition, necessary      6 216
Condition, necessary and sufficient      41 46 47 50 51 56 58 64 194 206 215

Condition, quadratic      23
Condition, sufficient      46 78 113 160
Condition, Wieferich's      68 69 217
Congruence      xvii 13 14 16 20 33 43 47 48 56 59 71 72 81 100 145
Congruence conditions      78 94
Congruence constraints      78
Conjecture      156 157 163
Conjecture, Fermat's      1
Conjecture, Mordell's      xii
Conjecture, unsolved      216
Contradiction      51 56 65 88 89 97 120
Control parameter      177 178
Converse implication      48 205
Convolution      167 168 170
Convolution, complex      171
Convolution, cyclic      168 169
Convolution, digital      167
Convolution, finite discrete      167
Convolution, two-dimensional      170
Convolution, two-dimensional cyclic      170
Conway, J. H.      32 35 131
Cooklev, T. V.      170 217
Cooley, J. W.      167
coordinates      vii xiv 191
Cormack, G. V.      70 73
Correlation      167
Cosgrave      5
Counterexample      216
Coxeter, H. S. M.      39
Crandall, R.E.      5 7 43 68 159 171 173 209 210 217
Creutzburg, R.      166-168 170-173
Criterion, Brun's      113
Criterion, Euler's      23 30 42 64 71 137 140 151
Cryptography      13 173
cube      15 66 163 164 202 216
Cube, perfect      94
Cullen, J.      157
Cunningham, A. J.      4 153 157 208
Curve      vii ix xv 36 186
Curve, algebraic      xiv 184
Curve, cubic      vii
Curve, irregular      48
Curve, oriented      48
Curve, plane      xv
Curve, regular      48
CYCLE      54
Cyclic convolution property      165
Cycloid      vii xiv xv
Cylinder, infinite      13
D $\ddot{u}$ llmann, S.      154
de Bessy, B. F.      xi xiii xv 130
de Carcavi, P.      xiii
de Fermat, P.      vii-xvii 1 2 6 37 38 41 79 101 130 158 213 214 218-225
de la Vall $\acute{e}$ e Poussin      5
Decoding      170
Decomposition      17
Deconvolution      170
Dedekind      xiii
Degree      183
Degree, minimal      189
Denominator      7
density      22 75 76 159
Derivative      xiv
Descartes, R.      vii xiii xv xvi
Diagonal      196 197 203
Diameter      203
Dickson, L.E.      32 42 47 59 131 158 213 214 217
Diffie, W.      7
digit      29 36 94 161
Digit, binary      87-89 172
Digital computation      167
Dilcher, K.      5 32 68 210
DIMENSION      188 190
Dimitrov, V. S.      170 217
Diophantus      x xiv
Diophantus's       ix xi xii
Dirichlet, P. G. L.      xii 22
Discrete iteration      54 55
Divergence      179
Divisibility ix      60
Divisor      70 76 116 165 214
Divisor, composite      141
Divisor, greatest common      10 11 13 60 99
Divisor, nontrivial      13 63
Divisor, odd prime      151
Divisor, positive      150 183
Divisor, prime      4 69 84 143 144 145 214
Divisor, primitive prime      69 139 140 142-144 147 148 151
Divisor, proper      13
Divisor, proper prime      78
Divisor, smallest prime      162
dodecahedron      163 164
Doenias, J.      5 43 209
Donevsky, B.D.      170 217
Dong, P. P.      73
Doubling      184
Doubling, the period      177 184
Dubner, H.      154
Dudek, J.      58
Duparc, H. J. A.      131
Dyson, F.      39
EDGE      55 56
Edge, directed      55 56
Einstein, A.      xxi 158
Elliott, D.F.      168 171 217
ellipse      vii xiv
Encrypting messages      7
Equation, algebraic      182
Equation, binomial      198
Equation, Catalan      94 95 99 155
Equation, Diophantine      ix x 16 66 94 117
Equation, irreducible algebraic      184
Equation, linear      171
Equation, linear diophantine      12
Equation, logistic      3 165 177 179 182
Equation, nonlinear difference      177
Equation, of the second degree      192
Equation, partial differential      173
Equation, Pell      x
Equation, quadratic      199-201
Erd $\ddot{o}$ s, P.      101 104 105 113 115 116 39 132 159
Error-correcting codes      170
Euclid      2 194 215
Euclidean construction      2 3 33 159 187 193 194 202 204 205
Euler, L.      x xii xvi xvii 1-3 23 33 38 38 59 64 78 95 158 208 214 215
Eves, H.      26
Evolution      177
Exactly divides      13
Existence      15
Expectation, total      158
Face      164
Factor      3 4 43 60 66 67 71 110
Factor, largest prime      73 75 154
Factor, largest square      150
Factor, largest square-free      75
Factor, lucky Fermat      77-79
Factor, mutually coprime      155
Factor, nontrivial      5 7 8 40 213
Factor, odd      61
Factor, penultimate prime      4
Factor, prime      4 43 63 66 70 71 78 83 41 142 143 152-154 157-161 183 207 209-212
Factor, rational      111
Factoring      6 173 182 183
Factorization      2 4 7 22 38 60 63 153 39 213
Factorization, complete      3 41 148 159 184
Factorization, computer      163
Factorization, prime      163 181
Factorization, prime-power      19 21 34 42
Fagin, B.      171 217
Faltings, G.      xii

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