- Extensively covers the Catalan Conjecture and Mihăilescu’s subsequent proof
- Includes thorough exposition of cyclotomic fields
- Provides a bridge between number theory and classical analysis
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- About this book
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In 1842 the Belgian mathematician Eugène Charles Catalan asked whether 8 and 9 are the only consecutive pure powers of non-zero integers. 160 years after, the question was answered affirmatively by the Swiss mathematician of Romanian origin Preda Mihăilescu. In other words, 32 – 23 = 1 is the only solution of the equation xp – yq = 1 in integers x, y, p, q with xy ≠ 0 and p, q ≥ 2.
In this book we give a complete and (almost) self-contained exposition of Mihăilescu’s work, which must be understandable by a curious university student, not necessarily specializing in Number Theory. We assume a very modest background:a standard university course of algebra, including basic Galois theory, and working knowledge of basic algebraic number theory.
- Table of contents (13 chapters)
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A Historical Account
Pages 1-9
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Even Exponents
Pages 11-25
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Cassels’ Relations
Pages 27-35
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Cyclotomic Fields
Pages 37-48
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Dirichlet L-Series and Class Number Formulas
Pages 49-63
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Table of contents (13 chapters)
- Download Preface 1 PDF (1.3 MB)
- Download Sample pages 1 PDF (1.3 MB)
- Download Table of contents PDF (1.8 MB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- The Problem of Catalan
- Authors
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- Yuri Bilu
- Yann Bugeaud
- Maurice Mignotte
- Copyright
- 2014
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer International Publishing Switzerland
- eBook ISBN
- 978-3-319-10094-4
- DOI
- 10.1007/978-3-319-10094-4
- Hardcover ISBN
- 978-3-319-10093-7
- Softcover ISBN
- 978-3-319-36255-7
- Edition Number
- 1
- Number of Pages
- XIV, 245
- Number of Illustrations
- 3 b/w illustrations
- Topics
*immediately available upon purchase as print book shipments may be delayed due to the COVID-19 crisis. ebook access is temporary and does not include ownership of the ebook. Only valid for books with an ebook version. Springer Reference Works are not included.
