The Problem of Catalan
| Autor: | Yuri Bilu, Yann Bugeaud, Maurice Mignotte |
|---|---|
| EAN: | 9783319100944 |
| eBook Format: | |
| Sprache: | Englisch |
| Produktart: | eBook |
| Veröffentlichungsdatum: | 09.10.2014 |
| Kategorie: | |
| Schlagworte: | Algebraic number theory Catalan Conjecture Cyclotomic fields Galois Theory |
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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 Mihailescu. In other words, 32 - 23 = 1 is the only solution of the equation xp - yq = 1 in integers x, y, p, q with xy ? 0 and p, q = 2.
In this book we give 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.
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