The Problem of Catalan

Authors: Bilu, Yuri, Bugeaud, Yann, Mignotte, Maurice

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  • 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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  • ISBN 978-3-319-10094-4
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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 xpyq = 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)

Table of contents (13 chapters)
  • A Historical Account

    Pages 1-9

    Bilu, Yuri F. (et al.)

  • Even Exponents

    Pages 11-25

    Bilu, Yuri F. (et al.)

  • Cassels’ Relations

    Pages 27-35

    Bilu, Yuri F. (et al.)

  • Cyclotomic Fields

    Pages 37-48

    Bilu, Yuri F. (et al.)

  • Dirichlet L-Series and Class Number Formulas

    Pages 49-63

    Bilu, Yuri F. (et al.)

Buy this book

eBook n/a
  • ISBN 978-3-319-10094-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
Hardcover n/a
  • ISBN 978-3-319-10093-7
  • Free shipping for individuals worldwide
Softcover n/a
  • ISBN 978-3-319-36255-7
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
The Problem of Catalan
Authors
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