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The Problem of Catalan

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

  • 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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eBook 71,39 €
price for Spain (gross)
  • ISBN 978-3-319-10094-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 88,39 €
price for Spain (gross)
  • ISBN 978-3-319-10093-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 88,39 €
price for Spain (gross)
  • ISBN 978-3-319-36255-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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)

Buy this book

eBook 71,39 €
price for Spain (gross)
  • ISBN 978-3-319-10094-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 88,39 €
price for Spain (gross)
  • ISBN 978-3-319-10093-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 88,39 €
price for Spain (gross)
  • ISBN 978-3-319-36255-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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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 and Tables
3 b/w illustrations
Topics