Fermat's last theorem for amateurs:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2000
|
| Edition: | Corr. 2. print. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 382 - 395 |
| Physical Description: | XII, 407 S. Ill. |
| ISBN: | 0387985085 |
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MARC
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| 245 | 1 | 0 | |a Fermat's last theorem for amateurs |c Paulo Ribenboim |
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Record in the Search Index
| _version_ | 1804128430442151936 |
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| adam_text | Titel: Fermat s last theorem for amateurs
Autor: Ribenboim, Paulo
Jahr: 2000
Contents
Preface
Reader
v
vii
Acknowledgment xiii
The Problem 1
I. Special Cases 3
1.1. The Pythagorean Equation 3
1.2. The Biquadratic Equation 11
1.3. Gaussian Numbers 21
1.4- The Cubic Equation 24
1.5. The Eisenstein Field 41
1.6. The Quintic Equation 49
1.7. Fermat s Equation of Degree Seven 57
1.8. Other Special Cases 63
1.9. Appendix 71
x Contents
II. 4 Interludes 73
II. 1. p-Adic Valuations 73
II.2. Cyclotomic Polynomials 77
77.5. Factors of Binomials 79
II.4. The Resultant and Discriminant of Polynomials 95
III. Algebraic Restrictions on Hypothetical Solutions 99
777.7. The Relations of Barlow 99
III.2. Secondary Relations for Hypothetical Solutions 106
TV. Germain s Theorem 109
IV. 1. Sophie Germain s Theorem 109
IV.2. Wendt s Theorem 124
IV.3. Appendix: Sophie Germain s Primes 139
V. Interludes 5 and 6 143
V.l. p-Adic Numbers 143
A. The Field of p-Adic Numbers 143
B. Polynomials with p-Adic Coefficients 145
C. Hensel s Lemma 152
V.2. Linear Recurring Sequences of Second Order 156
VI. Arithmetic Restrictions on Hypothetical Solutions
and on the Exponent 165
VIA. Congruences 165
VI. 2. Divisibility Conditions 184
VI.3. Abel s Conjecture 195
VI.4- The First Case for Even Exponents 203
VII. Interludes 7 and 8 213
V77.7. Some Relevant Polynomial Identities 213
VII.2. The Cauchy Polynomials 220
Contents xi
VIII. Reformulations, Consequences, and Criteria 235
VIII. 1. Reformulation and Consequences of Fermat s Last
Theorem 235
A. Diophantine Equations Related to Fermat s Equation 235
Al. Lebesgue
A2. Christilles
A3. Perrin
A4. Hurwitz
A5. Kapferer
A6. Frey
B. Reformulations of Fermat s Last Theorem 247
VIII.2. Criteria for Fermat s Last Theorem 253
A. Connection with Euler s Totient Function 253
B. Connection with the Mobius Function 255
C. Proof that a Nontrivial Solution Cannot be in Arith-
metical Progression 255
D. Criterion with a Legendre Symbol 256
E. Criterion with a Discriminant 257
F. Connection with a Cubic Congruence 263
G. Criterion with a Determinant 266
H. Connection with a Binary Quadratic Form 267
I. The Non-Existence of Algebraic Identities Yielding
Solutions of Fermat s Equation 269
J. Criterion with Second-Order Linear Recurrences 270
K. Perturbation of One Exponent 272
L. Divisibility Condition for Pythagorean Triples 273
IX. Interludes 9 and 10 277
7X7. The Gaussian Periods 277
IX.2. Lagrange Resolvents and Jacobi Cyclotomic Function 282
X. The Local and Modular Fermat Problem 287
X.l. The Local Fermat Problem 287
X.2. Fermat Congruence 291
X.3. Hurwitz Congruence 304
X-4- Fermat s Congruence Modulo a Prime-Power 316
xii Contents
XI. Epilogue 359
XI. 1. Attempts 359
A. The Theorem of Kummer 360
B. The Theorem of Wieferich 361
C. The First Case of Fermat s Last Theorem for Infinitely
Many Prime Exponents 363
D. The Theorem of Faltings 363
E. The (abc) Conjecture 364
XI. 2. Victory, or the Second Death of Fermat 366
A. The Frey Curves 367
B. Modular Forms and the Conjecture of Shimura-Tani-
yama 369
C. The Work of Ribet and Wiles 373
XI. 3. A Guide for Further Study 375
A. Elliptic Curves, Modular Forms: Basic Texts 375
B. Expository 375
C. Research 378
XI.4- The Electronic Mail in Action 379
Appendix A. References to Wrong Proofs 381
7. Papers or Books Containing Lists of Wrong Proofs 382
II. Wrong Proofs in Papers 382
III. Insufficient Attempts 387
Appendix B. General Bibliography 389
7. The Works of Fermat 389
II. Books Primarily on Fermat 390
III. Books with References to Fermat s Last Theorem 391
IV. Expository, Historical, and Bibliographic Papers 392
V. Critical Papers and Reviews 395
Name Index 396
Subject Index 404
|
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| edition | Corr. 2. print. |
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| id | DE-604.BV013623686 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:49:07Z |
| institution | BVB |
| isbn | 0387985085 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009306437 |
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| physical | XII, 407 S. Ill. |
| publishDate | 2000 |
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| spelling | Ribenboim, Paulo 1928- Verfasser (DE-588)117719404 aut Fermat's last theorem for amateurs Paulo Ribenboim Corr. 2. print. New York [u.a.] Springer 2000 XII, 407 S. Ill. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 382 - 395 Fermat's last theorem Fermatsche Vermutung (DE-588)4154012-8 gnd rswk-swf Fermatsche Vermutung (DE-588)4154012-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009306437&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ribenboim, Paulo 1928- Fermat's last theorem for amateurs Fermat's last theorem Fermatsche Vermutung (DE-588)4154012-8 gnd |
| subject_GND | (DE-588)4154012-8 |
| title | Fermat's last theorem for amateurs |
| title_auth | Fermat's last theorem for amateurs |
| title_exact_search | Fermat's last theorem for amateurs |
| title_full | Fermat's last theorem for amateurs Paulo Ribenboim |
| title_fullStr | Fermat's last theorem for amateurs Paulo Ribenboim |
| title_full_unstemmed | Fermat's last theorem for amateurs Paulo Ribenboim |
| title_short | Fermat's last theorem for amateurs |
| title_sort | fermat s last theorem for amateurs |
| topic | Fermat's last theorem Fermatsche Vermutung (DE-588)4154012-8 gnd |
| topic_facet | Fermat's last theorem Fermatsche Vermutung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009306437&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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