| 书目名称 | Polynomial Diophantine Equations | | 副标题 | A Systematic Approac | | 编辑 | Bogdan Grechuk | | 视频video | | | 概述 | Studies Diophantine equations systematically, in order.Hundreds of equations are left as exercises, solutions provided.Contains a large collection of open problems of all levels of difficulty | | 图书封面 |  | | 描述 | .This book proposes a novel approach to the study of Diophantine equations: define an appropriate version of the equation’s size, order all polynomial Diophantine equations by size, and then solve the equations in order...Natural questions about the solution set of Diophantine equations are studied in this book using this approach. Is the set empty? Is it finite or infinite? Can all integer solutions be parametrized? By ordering equations by size, the book attempts to answer these questions in a systematic manner. When the size grows, the difficulty of finding solutions increases and the methods required to determine solutions become more advanced. Along the way, the reader will learn dozens of methods for solving Diophantine equations, each of which is illustrated by worked examples and exercises. The book ends with solutions to exercises and a large collection of open problems, often simple to write down yet still unsolved...The original approach pursued in this book makes it widely accessible. Many equations require only high school mathematics and creativity to be solved, so a large part of the book is accessible to high school students, especially those interested in mathemati | | 出版日期 | Textbook 2024 | | 关键词 | Diophantine equations; integer solutions; rational solutions; Hasse principle; quadratic reciprocity; Vie | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-031-62949-5 | | isbn_softcover | 978-3-031-62951-8 | | isbn_ebook | 978-3-031-62949-5 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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发表于 2025-3-21 19:11:10
