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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eBook 71,68 €
price for Spain (gross)
  • ISBN 978-3-319-10094-4
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Hardcover 103,99 €
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Softcover 88,39 €
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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)

Buy this book

eBook 71,68 €
price for Spain (gross)
  • ISBN 978-3-319-10094-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • Immediate eBook download after purchase and usable on all devices
  • Bulk discounts available
Hardcover 103,99 €
price for Spain (gross)
Softcover 88,39 €
price for Spain (gross)
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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