An introduction to Diophantine equations: a problem-based approach
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
Birkhäuser
2010
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 345 S. 235 mm x 155 mm |
| ISBN: | 9780817645489 |
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Record in the Search Index
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| adam_text | Titel: An introduction to Diophantine equations
Autor: Andreescu, Titu
Jahr: 2010
Contents
Preface v
I Diophantine Equations 1
I.I Elementary Methods for Solving Diophantine
Equations 3
1.1 The Factoring Method ................ 3
1.2 Solving Diophantine Equations Using Inequalities . 13
1.3 The Parametric Method................ 20
1.4 The Modular Arithmetic Method . . ........ 29
1.5 The Method of Mathematical Induction....... 36
1.6 Fermât s Method of Infinite Descent (FMID) .... 47
1.7 Miscellaneous Diophantine Equations....... . 58
÷ Contents
1.2 Some Classical Diophantine Equations 67
2.1 Linear Diophantine Equations............ 67
2.2 Pythagorean Triples and Related Problems..... 76
2.3 Other Remarkable Equations............. 88
1.3 Pell-Type Equations 117
3.1 Pell s Equation: History and Motivation.......118
3.2 Solving Pell s Equation................121
3.3 The Equation ax2 - by2 = 1 .............135
3.4 The Negative Pell s Equation.............140
1.4 Some Advanced Methods for Solving Diophantine
Equations 147
4.1 The Ring Z[z] of Gaussian Integers..........151
4.2 The Ring of Integers of Q[Vd]............162
4.3 Quadratic Reciprocity and Diophantine Equations . 178
4.4 Divisors of Certain Forms...............181
4.4.1 Divisors of a2 + b2...............182
4.4.2 Divisors of a2 + 2b2..............186
4.4.3 Divisors of a2 - 2b2............. . 188
II Solutions to Exercises and Problems 191
II.1 Solutions to Elementary Methods for Solving
Diophantine Equations 193
1.1 The Factoring Method................193
1.2 Solving Diophantine Equations Using Inequalities . 202
1.3 The Parametric Method................213
Contents xi
1.4 The Modular Arithmetic Method ..........219
1.5 The Method of Mathematical Induction.......229
1.6 Fermat s Method of Infinite Descent (FMID) . . . . 239
1.7 Miscellaneous Diophantine Equations........253
11.2 Solutions to Some Classical Diophantine
Equations 265
2.1 Linear Diophantine Equations............265
2.2 Pythagorean Triples and Related Problems.....273
2.3 Other Remarkable Equations.............278
11.3 Solutions to Pell-Type Equations 289
3.1 Solving Pell s Equation by Elementary Methods . . 289
3.2 The Equation á÷2 - by2 = 1 .............298
3.3 The Negative Pell s Equation.............301
11.4 Solutions to Some Advanced Methods in Solving
Diophantine Equations 309
4.1 The Ring Z[i] of Gaussian Integers..........309
4.2 The Ring of Integers of Q[Vd]............314
4.3 Quadratic Reciprocity and Diophantine Equations . 322
4.4 Divisors of Certain Forms...............324
References 327
Glossary 331
Index 341
|
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| discipline | Mathematik |
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| id | DE-604.BV037307491 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T23:21:43Z |
| institution | BVB |
| isbn | 9780817645489 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022462003 |
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| physical | XI, 345 S. 235 mm x 155 mm |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Birkhäuser |
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| spelling | Andreescu, Titu 1956- Verfasser (DE-588)12217805X aut An introduction to Diophantine equations a problem-based approach Titu Andreescu ; Dorin Andrica ; Ion Cucurezeanu New York, NY [u.a.] Birkhäuser 2010 XI, 345 S. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Diophantische Gleichung (DE-588)4012386-8 gnd rswk-swf Diophantische Gleichung (DE-588)4012386-8 s DE-604 Andrica, Dorin 1956- Verfasser (DE-588)113881789 aut Cucurezeanu, Ion Verfasser (DE-588)142975729 aut Erscheint auch als Online-Ausgabe 978-0-8176-4549-6 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022462003&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Andreescu, Titu 1956- Andrica, Dorin 1956- Cucurezeanu, Ion An introduction to Diophantine equations a problem-based approach Diophantische Gleichung (DE-588)4012386-8 gnd |
| subject_GND | (DE-588)4012386-8 |
| title | An introduction to Diophantine equations a problem-based approach |
| title_auth | An introduction to Diophantine equations a problem-based approach |
| title_exact_search | An introduction to Diophantine equations a problem-based approach |
| title_full | An introduction to Diophantine equations a problem-based approach Titu Andreescu ; Dorin Andrica ; Ion Cucurezeanu |
| title_fullStr | An introduction to Diophantine equations a problem-based approach Titu Andreescu ; Dorin Andrica ; Ion Cucurezeanu |
| title_full_unstemmed | An introduction to Diophantine equations a problem-based approach Titu Andreescu ; Dorin Andrica ; Ion Cucurezeanu |
| title_short | An introduction to Diophantine equations |
| title_sort | an introduction to diophantine equations a problem based approach |
| title_sub | a problem-based approach |
| topic | Diophantische Gleichung (DE-588)4012386-8 gnd |
| topic_facet | Diophantische Gleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022462003&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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