TY  - BOOK
AU  - Bilu,Yuri F.
AU  - Bugeaud,Yann
AU  - Mignotte,Maurice
TI  - Problem of Catalan
SN  - 9783319100937
U1  - 512.922 23
PY  - 2014///
CY  - New York :   
PB  - Springer,    
KW  - Consecutive powers (Algebra)
KW  - Number theory.
N1  - Includes bibliographical references and indexes; 1. A historical account --
 2. Even exponents --
 3. Cassels' relations --
 4. Cyclotomic fields --
 5. Dirichlet L-series and class number formulas --
 6. Higher divisibility theorems --
 7. Gauss sums and Stickelberger's theorem --
 8. Mihăilescu's ideal --
9. The real part of Mihăilescu's ideal --
10. Cyclotomic units --
11. Selmer group and proof of Catalan's conjecture --
12. The theorem of Thaine --
13. 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--
References--
Author Index--
Subject Index
N2  - In this book it is given a complete and (almost) self-contained exposition of Mihailescu’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
ER  -