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

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 257

Добавлена в каталог: 11.04.2008

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Предметный указатель

Fast coding      170
Feh $\acute{e}$ r, J.      144
Feigenbaum cascade      178
Feigenbaum, M. J.      177 178 184
Ferentinou - Nicolacopoulou, J.      155
Fermat's assertion      49
Fermat, C. - S.      viii ix xiii
Fermat, P.      see de Fermat
Field      187 191
Field, complex      187
Field, complex number      167
Field, extension      187 188 192
Field, finite-dimensional      189
Filter      170
Filtering      171
Filtering, data      167
Filtering, digital      170
Fine structure of the curve      185
Flammenkamp, A.      82
Form, canonical      179
Form, linear      73
Formula, asymptotic      75
Formula, Gauss      5 19
Formula, Heron's      98
Formula, Lucas      1
Formula, recurrence      26
Formula, Stirling's      83
Formula, symmetric      100
Fractal      179
Function, arithmetic      144
Function, Carmichael's lambda      21 136 145
Function, decreasing      74
Function, Euler totient      19 20 22 77 85 102 117 192
Function, exponential      xiv
Function, hashing      174 176
Function, M $\ddot{o}$ bius      147
Function, minimal perfect hashing      174 176
Function, number-theoretic      144
Function, ordered minimal perfect hashing      176
Function, pairwise coprime transformation      175
Function, perfect hashing      174
Function, Riemann $\zeta$       10
G $\acute{e}$ rardin      208
Gallot      5 154
Game, computer      173
Gardner, M.      35 80
Gauss, C.F.      xi xvii 1-4 9 13 18 19 24 32 33 35 187 193-197 201 205 207
Gaussian notation      14
Generator of pseudorandom numbers      165 174
Geometric interpretation      11 12 16 17 27 47 56 95 180
Geometry      33 35
Geometry, analytic      vii xii
Geometry, non - Euclidean      37
Germain, S.      xii
Gillispie, Ch. C.      viii
Goldbach, Ch      33
Golden section      203
Golomb's corollary      108
Golomb, S.W.      65 70 77 104 108 162
Good, I.J.      114
Gorshkov, A. S.      167 171 173 217
Gostin, G. B.      5 68 160 210
Gottlieb, C.      3 204
Graham, R. L.      115
Granville, A.      136
Graph      54
Graph, associated      57
Graph, asymmetric      57
Graph, binary      55 56
Graph, iteration      55
Graph, nondirected      55
Graph, of the function      177
Graph, rotationally symmetric      57
Graph, topologically equivalent      56
Group      192
Group, abelian Galois      192
Group, cyclic      48 192
Group, finite      192
Group, of permutations      192
Growth, exponential      105
Grundmann, H. - J.      166-168 170-173
Grytczuk, A.      26 28 46 73 154
Grytczuk, J.      46
Gulliver, T. A.      154
Gutfreund, H.      17
Guy, R.K.      32 35 68 131 158 164
H $\acute{e}$ rigone, P.      xiv
hadamard      5
Hallyburton, J. C.      5 210
Hamada, H.      171
Hamilton, W. R.      xvi
Hamiltonian path      48
Harborth, H.      90 91 93
Hardware      170
Hardy, G.H.      5 32 33 38 39 158
Hashing      174
Heilman, M. E.      7
Helix      13
Heptakaidecagon      203
Hermes, J.      204
Hewgill, D.      35 80
Hilbert, D.      147
Hilton, P.      33
Hiriart - Urruty, J.-B.      221
Hoggatt, E.V.      114
Hooley, C.      157
Hsu, I. S.      171
Huard, J. G.      86
Hungerford, T. W.      188 192
Huron, R.      viii
Hurwitz, A.      5 43 209
Huygens, Ch.      xii xv xvi
Hyperbola      vii xii xiv
Hypotenuse      98
icosahedron      163 164
Ideal, Stickelberger      154
Identity, convolution      168
Identity, Vi $\grave{e}$ te's      50
Imaginary unit      171
Incongruence      91-93
INDEX      185
Induction      13 17 50 67 106
Induction step      191
Induction, complete      xiii
Induction, incomplete      xiii
Induction, mathematical      xiii
Inequality, Chleboun's      61
Inequality, sharp      61 63
Inequality, triangular      98 100
Inkeri, K.      46
Input data      8
Integer part      5 6
Integer, algebraic      98
Integer, composite      43 137 141
Integer, even      52 96 153
Integer, Gaussian      189
Integer, non - Sierpi $\acute{n}$ ski odd      159
Integer, nonnegative      72 96 114 120 125
Integer, odd      62 140
Integer, odd composite      137 141
Integer, perfectly symmetric      57
Integer, positive      x 28 49 72 74 107 113 116 140 145 156 205
Integer, square-free      x
Integers, amicable      101
Integers, coprime      11 20 134 140
Integers, coprime positive      105 205
Integers, relatively prime      11
Inverse      166
Ireland, K.      22 65
Irrationality      104 107 110 113 116

Jacobi, C. G. J.      x
Jacobson, E.      136 137
Jaeschke, G.      73 176
Jarden, D.      132
Jeans, J.H.      131-133
Jiang, Z. R.      170
Jim $\acute{e}$ nez Calvo, I.      154
Jones, P.      147 152
Jones, R.      56 57 162
Josephy, M.      206
Judd, J. S.      4
K $\check{r}\acute{\imath}\check{z}$ ek, M.      20 32 40 50 60 67 70 77 159 160 163
K $\check{r}\acute{\imath}\check{z}$ ek, P.      163
Kawatani, T.      7 32
Keller, W.      1 5 32 37 39 40 46 70 73 152-154 156 157 162
Kepler, J.      xiv
Key      174 176
Kida, Y.      148
Kiss, E.      31 37
Kiss, P.      144
Klein, F.      32 201
Kline, M.      33
Knuth, D. E.      7 43
Koblitz, N.      7 25
Koch, M.      93
Korselt, A.      136
Kra $\ddot{\imath}$ tchik, M.      1 39 210 214 216
Kravchenko, V. F.      167 171
Krishna, H.V.      66 82 97
Kronecker delta      169
Kronecker, L.      117
Ku $\check{c}$ era, R.      168 217
Kummer, E. E.      xii 86
La $\check{s}\check{s}\acute{a}$ k, M.      20
Labunets, V. G.      171
Lagrange, J. L.      x xi xvi 214
Lam $\acute{e}$ , G.      xi xii
Landry, F.      3 208
Larras, J.      60
Law of quadratic reciprocity      24 44
Law of refraction      xv
Law, strong of small numbers      164
Le Lasseur      208
Le, M.      73
Lebesgue, V.A.      95 99
Lee, Y. C.      170
Lef $\acute{e}$ vre, R.      224
Legendre, A.M.      xii
Lehmer, D.H.      5 42 63 70 131 142 153 212 214
Leibniz, G. W.      xiv 131
Leibowitz, L.M.      170
Lemniscate      35 36
Length, maximum transformation      165
Length, transformation      165
Lenstra, A. K.      4 8 38 42 66 67 208
Lenstra, H. W.      4 7 8 38 42 46 47 66 67 138 159 208
Lepka, K.      17
LeVeque, W. J.      68 151
Leyendekkers, J. V.      32
Li, L.      8
Li, W.      170
Lidl, R.      148
Ligh, S.      147 152
Linear space      188 190
Little, W. A.      17
Liu, P.      3
Logarithm      73
Luca, F.      20 73 77 82 86 97 101 117 144 146 154 163
Lucas's Lemma      81
Lucas's primality test      41
Lucas, E.      39 41 43 46 59 60 81 210
Luck $\acute{a}$ , M.      170
M $\ddot{o}$ bius      150
M $\k{a}$ kowski, A.      28 135
Macrae, N.      165
Magnitude      8
Mahler, K.      115
Mahnke, D.      131
Mahoney, M. S.      viii 41 94 130 213 214
Maillard, J. - M.      177
Malm, D. E. G.      138
Malo, E.      133
Manasse, M. S.      4 8 38 42 66 67 208
Mandelbrot, B.      179
Mann, H. B.      89
Map, inverse      192
Map, nonzero      192
Martzloff, J. - C.      14 16 80
Maruyama, S.      7 32
Matrix, identity      169
Matrix, inverse transformation      168
Matrix, nonsingular      168
Matrix, transformation      168
Mayer, E.      5 43 209
McClellan, J.H.      170
McDaniel, W. L.      96
McIntosh, R.      46 210
McLaughlin, P. B.      5 68 160 210
Median      98
Medicine      167
Meissner      68
Mersenne, M.      xv 41 213 217
Mesh, square      11
Method, Baker's      73
Method, continued fraction      3
Method, elliptic curve      4 8
Method, factorization      3 6 7
Method, Fermat factorization      7
Method, mathematical      ix
Method, Monte Carlo      173
Method, numerical      ix
Method, of infinite descent      xiii
Method, Pollard's rho      4
Method, RSA      13
midpoint      203
Mignotte, M.      115 152
Miller, G.L.      7
Min, B. K.      170
Model, chiral Potts      165 177
Model, mathematical      177
Modem      171
Monier, L.      138
Montgomery, P.L.      8 19 20 24 25 32 68
Morain, F.      4 5 208
Morehead, J. C.      5 63
Morh $\acute{a}\check{c}$ , M.      171
Morikawa, Y.      171
Morimoto, M.      148 154
Morrison, M. A.      3 208
Multiple, least common      10 13 104
Multiplication      167
Multiplication, by powers      172
Multiplication, fast      165
Multiplication, of large numbers      173
Multiplicity      78 143 144 151
Narkiewicz, W.      19 32
Naur, T.      1
Neal, L.      152
Negation      172
Newton, I.      xv
Niederreiter, H.      148
Niven, I.      19 20 24 25 32
Norm      170
Norrie, C.      5 43 209
Number, -gonal      x
Number, algebraic      189
Number, binary      3
Number, Carmichael      131 135 136
Number, complex      10 167 180 187-191
Number, composite      2 3 9 36 143 159

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