
The Problem of Catalan
Springer (Publisher)
Published on 27. October 2014
Book
Hardback
XIV, 245 pages
978-3-319-10093-7 (ISBN)
Description
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 Mihailescu. In other words, 3<sup>2</sup> - 2<sup>3</sup> = 1 is the only solution of the equation x<sup>p</sup> - y<sup>q</sup> = 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 Mihailescu'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.
More details
Product info
Book
Language
English
Place of publication
Cham
Switzerland
Target group
Research
Illustrations
3 s/w Abbildungen, 1 s/w Tabelle
1 schwarz-weiße Tabellen, Bibliographie
Dimensions
Height: 244 mm
Width: 164 mm
Thickness: 19 mm
Weight
525 gr
ISBN-13
978-3-319-10093-7 (9783319100937)
DOI
10.1007/978-3-319-10094-4
Schweitzer Classification
Other editions
Additional editions

Yuri F. Bilu | Yann Bugeaud | Maurice Mignotte
The Problem of Catalan
Book
09/2016
Springer
€53.49
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Yuri F. Bilu | Yann Bugeaud | Maurice Mignotte
The Problem of Catalan
E-Book
10/2014
1st Edition
Springer
€53.49
Available for download
Content
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.- Mihailescu's Ideal.- The Real Part of Mihailescu'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.