The Problem of Catalan

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 (al...

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Bibliographic Details
Call Number:Libro Electrónico
Main Authors: Bilu, Yuri F. (Author), Bugeaud, Yann (Author), Mignotte, Maurice (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:Inglés
Published: Cham : Springer International Publishing : Imprint: Springer, 2014.
Edition:1st ed. 2014.
Subjects:
Number theory.
Universal algebra.
Algebra.
Number Theory.
General Algebraic Systems.
Online Access:Texto Completo
Table of Contents:
  • An Historical Account
  • Even Exponents
  • Cassels' Relations
  • Cyclotomic Fields
  • Dirichlet L-Series and Class Number Formulas
  • Higher Divisibility Theorems
  • Gauss Sums and Stickelberger's Theorem
  • Mihăilescu's Ideal
  • The Real Part of Mihăilescu's Ideal
  • Cyclotomic units
  • Selmer Group and Proof of Catalan's Conjecture
  • The Theorem of Thaine
  • Baker's Method and Tijdeman's Argument
  • Appendix A: Number Fields
  • Appendix B: Heights
  • Appendix C: Commutative Rings, Modules, Semi-Simplicity
  • Appendix D: Group Rings and Characters
  • Appendix E: Reduction and Torsion of Finite G-Modules
  • Appendix F: Radical Extensions.

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