| 书目名称 | The Problem of Catalan | | 编辑 | Yuri F. Bilu,Yann Bugeaud,Maurice Mignotte | | 视频video | | | 概述 | Extensively covers the Catalan Conjecture and Mihailescu’s subsequent proof.Includes thorough exposition of cyclotomic fields.Provides a bridge between number theory and classical analysis.Includes su | | 图书封面 |  | | 描述 | .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 other words, 3.2. – 2.3. = 1 is the only solution of the equation .x.p. – .y.q. = 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 Mihăilescu’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.. | | 出版日期 | Book 2014 | | 关键词 | Algebraic number theory; Catalan Conjecture; Cyclotomic fields; Galois Theory | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-319-10094-4 | | isbn_softcover | 978-3-319-36255-7 | | isbn_ebook | 978-3-319-10094-4 | | copyright | Springer International Publishing Switzerland 2014 |
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发表于 2025-3-21 19:11:30
