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| Stewart I., Tall D. — Algebraic Number Theory and Fermat's Last Theorem |
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| Предметный указатель |
 -periodic 245
(a, b, c) Conjecture 267
a-powered number 265
ABC-Conjecture 267
Abel, Niels Henrik 243 263
Addition theorem 243
Affine plane 216
Al-Khowarizmi, Mohammed 1
Algebra 1
algebraic 4 21 36
Algebraic integer 4 9 35 42 43 73
Algebraic number 35 43
Algebraic number held 35
Algebraically closed 13
Algorithm, division 14
Algorithm, Euclidean 15
Analytic class-number formula 197
Ascending chain condition 80
Associate 76
Automorphic function 205
Babylonian 1
Basic exponent 266
Basis 27 45
Beal Conjecture 267
Beal, Andrew 267
Bernoulli number 197 198
Beukers, Frits 264
Bezout’s Theorem 227
Bilinear map 251
Birkhoff, George 203
Bounded 129
Breuil, Christophe 263
Carcavi, Pierre de 143
Cardano, Girolamo 2
Catalan conjecture 264
Catalan problem 263
Cauchy, Augustin-Louis 243 274
Centrally symmetric 139
Characteristic 13
Class number problem 179
Class-group 151 152 157
Class-number 151 152 157 176 177 197
Coates, John 208 209
Complex line 213
Complex projective line 218
Complex projective plane 218
Complex projective point 218
Conductor 260
conformal 251 255
conic 214 215
Conic section 214
conjugate 38
Conrad, Brian 263
Constant 14
Convex 139
Coprime 15 89
Cubic 14
Cusp 223 256
Cusp form 259 262
Cyclotomic field 122
Cyclotomic number field 256
Darmon, Henri 264
Dedekind ring 106
Dedekind zeta-function 197
Dedekind, Richard 5 101 102 105 201
Degree 14 20
Diamond, Frederick 263
Dickson, Leonard Eugene 93 201
DIMENSION 129
Diophantine equation xi 1 96 222 230 243 263 266
Diophantus 2 235
Diophantus of Alexandria xi 1
Dirichlet L-series 197
Dirichlet, Peter Lejeune 185 293
Dirichlet’s units theorem 293 296 300
Discrete 130
Discriminant 38 40 46 48 63 68 115 155 207 248 260
Distance 149
Divide 13
Domain 10 12 79
Domain, Euclidean 90 91
Domain, noetherian 80
Domain, principal ideal 90
Domain, unique factorization 89—91
Doubly periodic 244 246 247
Eigenform 259
Eisenstein series 247
Eisenstein, F.G. 75 87 274
Eisenstein’s Criterion 18 64
Elkies, Noam 231
Elliptic curve 205 213 222 224 248 250 258 259
Elliptic curve, group structure on an 226
Elliptic function 235 243
Elliptic integral 243 244
Elliptic modular function 235 254 256
Equivalent 152
Euclidean function 90 91
Euler function 276
Euler, Leonhard 3 73 75 143 144 184 257 273 276
Euler’s conjecture 230
Euler’s criterion 284
EXPONENT 277
Extension, finite 21
Factor 13
Factor, proper 13
Factorization 10 13 18 35 73 80—82 121 169
Faltings, Gerd 209—211
Fermat equation 186 193 262
Fermat — Catalan Conjecture 264 268
Fermat, Pierre de 2 6 75 94 143 144 183 186 257
Fermat’s Last Theorem xii 2 3 5 6 9 75 151 183 196 201 205 208 250 256 257 262 263 267 274
Fermat’s Last Theorem, n=4 186
Fermat’s Last Theorem, sketch proof of 261
Field 10 12
Field extension 20
Field of fractions 12
Field polynomial 39 40
Field, cyclotomic 64
Field, Gaussian 63
Field, quadratic 61 91 169
Finitely generated 12
Finitely generated R-module 25
Flach, Mattheus 209 211
Fleck, Albert 202
Formal derivative 16
Four-squares theorem 143
Fractional ideal 101
Frey curve 207 208 260
Frey elliptic curve 235 256 257 262
Frey, Gerhard 207 257
Frye, Roger 232
Function, doubly periodic 242
Function, meromorphic 244
Fundamental domain 131 132 154 253
Galois, Evariste 263
Gauss, Carl Friedrich 3 4 75 86 179 243 273 284 286 288
Gaussian integer 4 63 75
Gauss’s criterion 285
Generate 11 25 129
Genus 204 262
Geometric representation 148
Germain, Sophie 184 201
Godfield, Dorian 179
Granville, Andrew 264
Greatest common divisor 114
Gross, Benedict 179
Group, abelian 275
Group, additive 26
Group, circle 132
Group, finitely generated abelian 27 32
| Group, free abelian 26 28 129
Group, of units 77 295 300
Group, symmetric 22
Hecke operators 259
Hellegouarch, Yves 257
Highest common factor 15
Hilbert, David 5 161
Homogeneous coordinates 218 219
Hornomorphism 11
Ideal 11 102 103 201
Ideal number 5 101 102 151 201
Ideal, fractional 107 110 151
Ideal, maximal 105
Ideal, prime 105 107 110
Ideal, principal 158
Image 11
INTEGER 45 62
Integral basis 46 63
Integral domain 10
Invariant 251
Irreducible 14 17 74 80 82 87
Isomorphism 11
J-invariant 260 261
Jacobi, Carl Gustav Jacob 243 274
Jensen, Johann Ludwig Wilhelm Waldemar 185
Katz, Nick 210
Kernel 11
Kronecker, Leopold 274
Kummer, Ernst 3 5 75 101—103 123 151 162 183 185 196 201 203 274
Kummer’s Lemma 189 191
Kummer’s Theorem 193
Lagrange, Joseph-Louis 144 184
Lame, Gabriel 5 75 185
Langlands, Robert 211
Lattice 129 130 140 153 245 246 251 252 296 298
Least common multiple 114
Legendre normal form 249
Legendre symbol 281 289
Legendre, Adrien-Marie 3 185 201 243 244 249 273 283
Length 149
Level 256 262
Level Reduction Conjecture 262
Lexicographic order 24
Lindeinann, Ferdinand 202
Line at infinity 216
Linear 14
Linearly independent 27
Liouville, Joseph 5 185 250 274
Local coordinate map 255
Logarithmic representation 295
Logarithmic space 294 295
Lowest common multiple 89
Maximal condition 80
Mazur, Barry 230
Meromorphic 246
Mersenne, Marin 143
Minimal discriminant 260
Minimum polynomial 21 40 64
Minkowski, Hermann 139 142
Minkowski’s constants 172 175
Minkowski’s theorem 140 142 145 151 153 154 173 175 293 295
Mirimanoff, Dimitri 186 201
Miyaoka, Yoichi 209
Mobius map 251
Mobius transformation 205
Modular 258 259 262
Modular curve 256
Modular domain 253
Modular form 262
Modular function 205 250 261
Modular group 252
Monic 21
Monomorphism 11 38
Mordell conjecture 204 205
Mordell, Louis 204
Mordell’s theorem 229
Multi-valued 254
Multiplicity 16
Nagell, Trygve 96
Newton, Isaac 222
Noether, Emmy 80
Non-singular 223
Norm 49 82 115 146
Norm-Euclidean 93
Normal form 214 215
Number field 36
Overlap map 255
Parallel line 217
Parametrization 238 243 248
Parametrize 259
Patch 255
Period parallelogram 245
Poincare, Henri 204 205
Point at infinity 216
Pole 242
Polynomial 14
Polynomial, elementary symmetric 23
Polynomial, symmetric 22
Prime 3 74 75 87 142 169
Prime factorization 110
Prime number 73
Prime subfield 13
Prime, regular 193
Primitive root 276
Principal fractional ideal 152
Principal ideal 12 103 116
Projection 216
Projective line 215
Projective point 215
Projective special linear group 252
Projective transformation 216
Projectively equivalent 216
Pythagoras xi 1 129
Pythagorean 1
Pythagorean equation 236 238 239 241 243
Pythagorean triad 1 2
Pythagorean triple 222 266
Quadratic 14
Quadratic reciprocity 204
Quadratic reciprocity law 273 286
Quadratic residues 273 283
Quartic 14
Quintic 14
Quotient module 25
Quotient ring 11
R-action 25
R-module 25
R-submodule 25
Radical 265
Ramanujan — Nagell Theorem 96
Ramanujan, Srinivasa 96
Rank 28
Rational conic 220
Rational elliptic curve 225
Rational integer 45
Rational line 220
Rational point 220
Real elliptic curve 225
Real projective plane 215
Reciprocity 3
Reducible 13
Reduction 19 258
Regular 193 198 223
Regular prime 5 185
Regulator 197
Residue 242
Residue, biquadratic 4
Residue, cubic 54
Residue, quadratic 3
Ribet, Kenneth 257 262
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