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.

Язык:

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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Предметный указатель

Number, composite Fermat      60 62 64 79 42 138 143 160 208
Number, composite Mersenne      138 217
Number, constructible      190 191
Number, Cullen      147 157
Number, Cunningham      153
Number, even      215
Number, even perfect      216
Number, Feigenbaum      178
Number, Ferentinou - Nicolapoulou      154
Number, Fermat      vii 1-257
Number, Fibonacci      11 117
Number, figurate      ix x
Number, generalized Fermat      85 108 147 153 154
Number, innocent-looking      5
Number, irrational      104
Number, large      173
Number, Lucas      117
Number, Mersenne      44 45 82 139 143 145 147 154 181 213 214 216 217
Number, Mersenne square-free      217
Number, multiply perfect      103
Number, natural      10 11 13 16 19 39 50 51 59 66 71 72 161 215
Number, non - Sierpi $\acute{n}$ ski      159
Number, not powerful      69
Number, odd      97 161
Number, odd prime      150
Number, pentagonal      95
Number, pentagonal Fermat      97
Number, perfect ix      215 216
Number, polygonal x      95
Number, positive      125
Number, prime      xvi 9 10 68 74 81 163
Number, pseudorandom      3 13 173
Number, quadri-composite      158
Number, rational      98 107 116 184 188-190
Number, real      113 167 187
Number, Rotkiewicz      144-146
Number, Sierpi $\acute{n}$ ski      72 73 159 165
Number, smallest Sierpinski      73
Number, square      95
Number, square-free      119 160
Number, triangular      82 95
Numbers, amicable ix      101
Numbers, consecutive composite      157
Numbers, coprime      15 19
Numbers, Fermat pairwise coprime      183 184
Numbers, friendly      ix
Numbers, pairwise coprime      15
Numbers, Pythagorean      ix
Nussbaumer, H. J.      166 170-172
octahedron      163 164
Odlyzko, A. M.      4 159 208
Olbers, H.      xi
One-to-one correspondence      186
Opolka, H.      32
Order      61
Order, multiplicative      17
Pad $\acute{e}$ approximation      115 116
Pair, amicable      101
Pair, twin prime      66
Pairs of Fermat numbers      185
Papademetrios, I.      70
Papadopoulos, J.      5 43 209
Pappus      xii
parabola      vii xii xiv 180
Paraboloid      xiv
Parallel implementation      170
Parametrization      101
Pascal, B.      vii xii xv xvi
Pascal, E.      xii
Pattern recognition      167
Paxson, G.A.      5 43
Pearce, J.      56 57 162
Pedersen, J.      33
Pei, D. Y.      171
Pell, J.      x
Pepin, P.      41-43
Period      180-186
Period, minimal      180 181 183
periodicity      182
Permutation      48
Pervouchine      210
Peterson, A. M.      170
Petr, K.      47 48
Physical particles      17
Pierpont, J.      187 205
Pocklington, H. C.      70
Point, accumulation      177
Point, bifurcation      177
Point, Fermat      ix x
Point, fixed      54
Point, lattice      12
Pollard, J. M.      3 4 7 8 38 42 66 67 208
Polygon, constructible regular      205
Polygon, regular      2 33-35 85 97 109 117 159 164 191 194
Polygonal shape      96
Polyhedra, Platonic      163 164
Polyhedron, regular      163 164
Polynomial time      8
Polynomial, algebraic      xiv
Polynomial, cyclotomic      148 150 181-186 192
Polynomial, fundamental symmetric      85
Polynomial, in two variables      182
Polynomial, irreducible      192
Polynomial, irreducible lower-order      183
Polynomial, minimal      189 190 192
Polynomial, monic      98 189
Polynomial, nonzero      189
Pomerance, C.      7 8 47 68 135 136 138 139 152 159 173
Porubsk $\acute{y}$ , S.      20
Poulet, P.      131
Power      31 152
Power, composite prime      152
Power, higher      121-124 126-129
Power, negative      173
Power, perfect      94 150 152 155
Power, prime      97-99 149
Precision, finite      167
Primality      5 7 47 50 51 56 58 73
Primality testing      6 41 71 153 173
Prime      xii xvi 2 3 9 41 45-47 56 59 63 70 111 147 148 163 165 169 181
Prime, Cullen      157
Prime, elite      44 163
Prime, Fermat      1-3 54-57 85 88 91 93 97 99 109 110 117 118 120 125 144 157-159 163 184 194 206 207
Prime, irregular      xii
Prime, Mersenne      153 154 213-217
Prime, odd xv      51 53 56 87 140 155 156
Prime, probable      137 138 148 154
Prime, Sophie Germain      54 215
Prime, Wieferich's      68 69
Principle      164 206
Principle, Dirichlet pigeonhole      111
Principle, Fermat      vii xvi
Principle, well-ordering      xiii 11
probability      xvi 137 138 158
Problem, algebraic      205
Problem, deconvolution      171
Problem, four-line      xv
Problem, geometric xv      205
Problem, of the duplicated cube      202
Processing, digital signal      3 165
Processing, image      167
Product, infinite      113
Product, pointwise      168
Progression      178
Progression, arithmetic      22 77 139
Progression, geometric      169 178
Projection, orthogonal      203
Proth, F.      43 70
Pseudoprime      3 36 37 44 47 131 135 137 139 141 142 149 150 152 153 165 216
Pseudoprime, absolute      135 137

Pseudoprime, Euler      137-139 150 151
Pseudoprime, Fermat       136 137
Pseudoprime, for the function      144
Pseudoprime, odd      133
Pseudoprime, strong      137-139 147 150-152
Pseudoprime, to the base      137
Qin, J.      16
Quadratic nonresidue      23 30 44 50 52 54 174
Quadratrix      xiv
Quadrature      xiv
Quantization      167
Quotient, Fermat      17
Rabin, M. O.      47 138
Racli $\k{s}$ , N.      30
Radar      171
Rademacher, H.      32 201
Radovici - M $\breve{a}$ rculescu, P.      82 97
Rao, K.R.      168 171 217
ratio      154
Rationality      109
Reciprocal      104 109
Record      174
Reed, I. S.      170 171
Regular $2^{i}n$ -gon      205
Regular -gon      3 34 203-205
Regular -gon      48
Regular 15-gon      205
Regular 17-gon      3 194 196 204
Regular 257-gon      3 34 204
Regular 60-gon      33
Regular 65537-gon      3 34 204
Regular 7-gon      3
Regular 9-gon      3 205
Regular heptadecagon      33 34 193 197 198 203
Regular heptagon      194
Regular nonagon      194
Regular pentagon      3 34 198 202 203
Regular triangle      34 198
Reid, C.      32 194
Relation, divisibility      96
Relation, recurrence      27
Relation, reflexive      14
Relation, symmetric      14
Relation, transitive      14
Remainder      11 15 16 55-57 173-176 202
Repeller-curve      185
Representation, balanced      168
Representation, binary      121
Residue, th power      64
Residue, cubic      64
Residue, nonnegative      94
Residue, nonzero      202
Residue, of modulo       13
Residue, quadratic      23 24 50 64 100 120
Ribenboim, P.      32 54 60 67-69 95 131 135 136 155 214-217
Richelot, F. J.      204
Richmond, H. W.      203
Rickert, N.W.      5
Riesel, H.      5 8 9 23 32 142 154 158 40 210 214
Ripley, B. D.      13 174
Rivest, R. L.      7 13
Robbins, N.      32 33 47 215
Roberval, G. P.      viii xii xv
Robinson, R. M.      5 36 64 70 157
Rollet, G.      177
Root      2 189 190 198 201 202 205
Root, incongruent primitive      20
Root, of unity      191
Root, primitive      9 18 20 22 24 30 41 42 50 54 56 64 145 174 186 192 201
Root, smallest primitive      202
Root, square      6 171 197
Rosen, M.      22 35 36 65
Rosser, J. B.      103
Rotation      48
Rotkiewicz, A.      43 68 131-133 139 144 217
Round-off error      167 171
Ruler      2 3 33-35 85 109 117 187 190-192 194 197 202 205 206
Rumely, R. S.      47 138
Rvachev, V. A.      171
Rvachev, V. L.      171
S $\acute{a}$ ndor, J.      113
Samis      131
Satyanarayana, M.      97
Sch $\ddot{o}$ nhage, A.      165 167 173
Scharlau, W.      32
Scheme, hashing      3 165 174
Scheme, iteration      54 55
Schinzel, A.      140
Schneeberger, W. A.      131
Schoenfeld, L.      103
Scholtz, R. A.      170
Schram, J. M.      26
Schroeder, M. R.      5 16 32 186 204 213
Scott      154
Selfridge, J.L.      4 5 41 43 63 70 73 135 137-139 142 152 153 158 208-210 212 214
Semiperimeter      97
SEQUENCE      46 72 113 179 180
Sequence, bounded      179
Sequence, cyclic      54
Sequence, deterministic      173
Sequence, Fibonacci      114 115
Sequence, increasing      104 113
Sequence, Lucas      114 119 182
Sequence, monotone      159
Sequence, monotonically increasing      35
Sequence, of positive integers      113
Sequence, of pseudorandom numbers      174
Sequence, of random numbers      173
Sequence, periodic      57 174
Sequence, pseudorandom      173
Set, covering      72 73
Set, finite      54
Set, fractal      35 179
Set, key      174
Set, linearly independent      188 189
Set, Mandelbrot      179 180
Set, of positive integers      75
Set, of prime numbers      75
Set, of primes      22 76
Set, Sierpi $\acute{n}$ ski fractal      35
Shamir, A.      7 13
Shanks, D.      32 89 147 152 158
Shannon, A. G.      32
Shippee, D. E.      5
Shorey, T. N.      70
Sierpi $\acute{n}$ ski, W.      20 29 32 37 41 49 60 63 70 71 133 156 158
Sieve, number field      4
Sieve, of Eratosthenes      9
signal      166-168 170
Signal, complex      171
Signal, digital      167
Signal, filtering      170
Signal, periodic      168
Signal, transformed      168
Simulation of physical processes      173
Singh, S.      xi
Sino-representation      16
Skula, L.      154
Sloane, N. J. A.      131
Solovay, R.      137
Solution, analytic      xv
Solution, computable      85
Solution, general      15
Solution, integer      12
Solution, nonconstant periodic      178
Solution, nonperiodic      180 181
Solution, nontrivial      85
Solution, periodic      179-184 186
Solution, trivial      181 183
Solution, true      8

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