Overview
Extensively covers the Catalan Conjecture and Mihailescu’s subsequent proof
Includes thorough exposition of cyclotomic fields
Provides a bridge between number theory and classical analysis
Includes supplementary material: sn.pub/extras
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Table of contents (13 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: The Problem of Catalan
Authors: Yuri F. Bilu, Yann Bugeaud, Maurice Mignotte
DOI: https://doi.org/10.1007/978-3-319-10094-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2014
Hardcover ISBN: 978-3-319-10093-7Published: 27 October 2014
Softcover ISBN: 978-3-319-36255-7Published: 10 September 2016
eBook ISBN: 978-3-319-10094-4Published: 09 October 2014
Edition Number: 1
Number of Pages: XIV, 245
Number of Illustrations: 3 b/w illustrations
Topics: Number Theory, General Algebraic Systems, Algebra