Advertisement

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

Industry Sectors
Pharma
Finance, Business & Banking
Telecommunications
Aerospace