| 書目名稱 | Elements of Number Theory | | 編輯 | John Stillwell | | 視頻video | http://file.papertrans.cn/308/307620/307620.mp4 | | 概述 | Includes supplementary material: | | 叢書名稱 | Undergraduate Texts in Mathematics | | 圖書封面 |  | | 描述 | This book is intended to complement my Elements oi Algebra, and it is similarly motivated by the problem of solving polynomial equations. However, it is independent of the algebra book, and probably easier. In Elements oi Algebra we sought solution by radicals, and this led to the concepts of fields and groups and their fusion in the celebrated theory of Galois. In the present book we seek integer solutions, and this leads to the concepts of rings and ideals which merge in the equally celebrated theory of ideals due to Kummer and Dedekind. Solving equations in integers is the central problem of number theory, so this book is truly a number theory book, with most of the results found in standard number theory courses. However, numbers are best understood through their algebraic structure, and the necessary algebraic concepts- rings and ideals-have no better motivation than number theory. The first nontrivial examples of rings appear in the number theory of Euler and Gauss. The concept of ideal-today as routine in ring the- ory as the concept of normal subgroup is in group theory-also emerged from number theory, and in quite heroic fashion. Faced with failure of unique prime factoriz | | 出版日期 | Textbook 2003 | | 關鍵詞 | Euclidean algorithm; number theory; prime number | | 版次 | 1 | | doi | https://doi.org/10.1007/978-0-387-21735-2 | | isbn_softcover | 978-1-4419-3066-8 | | isbn_ebook | 978-0-387-21735-2Series ISSN 0172-6056 Series E-ISSN 2197-5604 | | issn_series | 0172-6056 | | copyright | Springer Science+Business Media New York 2003 |
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