The Problem of Catalan / / by Yuri F. Bilu, Yann Bugeaud, Maurice Mignotte
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| Autore: |
Bilu Yuri F
|
| Titolo: |
The Problem of Catalan / / by Yuri F. Bilu, Yann Bugeaud, Maurice Mignotte
|
| Pubblicazione: | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2014 |
| Edizione: | 1st ed. 2014. |
| Descrizione fisica: | 1 online resource (251 p.) |
| Disciplina: | 511/.6 |
| 512.72 | |
| Soggetto topico: | Number theory |
| Algebra | |
| Number Theory | |
| General Algebraic Systems | |
| Persona (resp. second.): | BugeaudYann |
| MignotteMaurice | |
| Note generali: | Description based upon print version of record. |
| Nota di bibliografia: | Includes bibliographical references and indexes. |
| Nota di contenuto: | 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. |
| Sommario/riassunto: | 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. |
| Titolo autorizzato: | The Problem of Catalan |
| ISBN: | 3-319-10094-7 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910299981103321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |