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Problem of Catalan

Author: Yuri F Bilu; Yann Bugeaud; Maurice Mignotte
Publisher: Switzerland : Springer, 2014.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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 this book we give a complete and (almost) self-contained exposition of Mihăilescu?s work, which must be understandable by a curious university student,  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Yuri F Bilu; Yann Bugeaud; Maurice Mignotte
ISBN: 9783319100944 3319100947 3319100939 9783319100937
OCLC Number: 893117743
Description: 1 online resource
Contents: An Historical Account --
Even Exponents --
Cassels' Relations --
Cyclotomic Fields --
Dirichlet L-Series and Class Number Formulas --
Higher Divisibility Theorems --
Gauss Sums and Stickelberger's Theorem --
Mihăilescu?s Ideal --
The Real Part of Mihăilescu?s Ideal --
Cyclotomic units --
Selmer Group and Proof of Catalan's Conjecture --
The Theorem of Thaine --
Baker's Method and Tijdeman's Argument --
Appendix A: Number Fields --
Appendix B: Heights --
Appendix C: Commutative Rings, Modules, Semi-Simplicity --
Appendix D: Group Rings and Characters --
Appendix E: Reduction and Torsion of Finite G-Modules --
Appendix F: Radical Extensions.
Responsibility: Yuri F. Bilu, Yann Bugeaud, Maurice Mignotte.

Abstract:

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 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 very modest background: a standard university course of algebra, including basic Galois theory, and working knowledge of basic algebraic number theory.

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