The Problem of Catalan

  • Yuri F. Bilu
  • Yann Bugeaud
  • Maurice Mignotte

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Yuri F. Bilu, Yann Bugeaud, Maurice Mignotte
    Pages 1-9
  3. Yuri F. Bilu, Yann Bugeaud, Maurice Mignotte
    Pages 11-25
  4. Yuri F. Bilu, Yann Bugeaud, Maurice Mignotte
    Pages 27-35
  5. Yuri F. Bilu, Yann Bugeaud, Maurice Mignotte
    Pages 37-48
  6. Yuri F. Bilu, Yann Bugeaud, Maurice Mignotte
    Pages 49-63
  7. Yuri F. Bilu, Yann Bugeaud, Maurice Mignotte
    Pages 65-73
  8. Yuri F. Bilu, Yann Bugeaud, Maurice Mignotte
    Pages 75-95
  9. Yuri F. Bilu, Yann Bugeaud, Maurice Mignotte
    Pages 97-115
  10. Yuri F. Bilu, Yann Bugeaud, Maurice Mignotte
    Pages 117-128
  11. Yuri F. Bilu, Yann Bugeaud, Maurice Mignotte
    Pages 129-134
  12. Yuri F. Bilu, Yann Bugeaud, Maurice Mignotte
    Pages 135-144
  13. Yuri F. Bilu, Yann Bugeaud, Maurice Mignotte
    Pages 145-158
  14. Yuri F. Bilu, Yann Bugeaud, Maurice Mignotte
    Pages 159-233
  15. Back Matter
    Pages 235-245

About this book

Introduction

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 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 very modest background: a standard university course of algebra, including basic Galois theory, and working knowledge of basic algebraic number theory.

Keywords

Algebraic number theory Catalan Conjecture Cyclotomic fields Galois Theory

Authors and affiliations

  • Yuri F. Bilu
    • 1
  • Yann Bugeaud
    • 2
  • Maurice Mignotte
    • 3
  1. 1.Institute of Mathematics of BordeauxUniversity of Bordeaux and CNRSTalenceFrance
  2. 2.IRMA, Mathematical InstituteUniversity of Strasbourg and CNRSStrasbourgFrance
  3. 3.IRMA, Mathematical InstituteUniversity of Strasbourg and CNRSStrasbourgFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-10094-4
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-10093-7
  • Online ISBN 978-3-319-10094-4
  • About this book
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