| 书目名称 | Catalan‘s Conjecture |
| 编辑 | René Schoof |
| 视频video | |
| 概述 | Provides complete proofs of a spectacular recent result in number theory.Accessible to the non-specialist: requires little more than a basic mathematical background and some knowledge of elementary nu |
| 丛书名称 | Universitext |
| 图书封面 |  |
| 描述 | .Eugène Charles Catalan made his famous conjecture – that 8 and 9 are the only two consecutive perfect powers of natural numbers – in 1844 in a letter to the editor of Crelle’s mathematical journal. One hundred and fifty-eight years later, Preda Mihailescu proved it...Catalan’s Conjecture presents this spectacular result in a way that is accessible to the advanced undergraduate. The author dissects both Mihailescu’s proof and the earlier work it made use of, taking great care to select streamlined and transparent versions of the arguments and to keep the text self-contained. Only in the proof of Thaine’s theorem is a little class field theory used; it is hoped that this application will motivate the interested reader to study the theory further...Beautifully clear and concise, this book will appeal not only to specialists in number theory but to anyone interested in seeing the application of the ideas of algebraic number theory to a famous mathematical problem.. |
| 出版日期 | Textbook 2008 |
| 关键词 | Algebra; Arithmetic; Catalan‘s conjecture; algebraic number theory; diophantine equations; number theory; |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-1-84800-185-5 |
| isbn_softcover | 978-1-84800-184-8 |
| isbn_ebook | 978-1-84800-185-5Series ISSN 0172-5939 Series E-ISSN 2191-6675 |
| issn_series | 0172-5939 |
| copyright | Springer-Verlag London 2008 |
发表于 2025-3-21 16:19:26
