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The Problem of Catalan.
・ISBN 978-3-319-10093-7 hard EUR 49.99
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| 著者・編者 | Bilu, Yuri F. / Bugeaud, Yann / Mignotte, Maurice, |
|---|---|
| 出版社 | (Springer International Publishing AG, SZ) |
| 出版年月 | 2014 |
| ページ数 | 245 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-22299＞ |
解説
In 1842 the Belgian mathematician Eugene 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.