Bilu, Yuri F., author.
Cham New York : Springer, [2014];©2014
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Notes:
- Includes bibliographical references and index.
- 1. An 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.
- 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.
Subjects:
- Consecutive powers (Algebra)
- Problem solving.
- Number theory.
- Mihăilescu, Preda, author.
- Catalan, Eugène Charles, 1814-1894.
Requested by Bloomberg, M.