Polynomial Diophantine Equations: A Systematic Approach
Polynomial Diophantine Equations: A Systematic Approach
English | 2024 | ISBN: 3031629485 | 824 Pages | PDF EPUB (True) | 96 MB
English | 2024 | ISBN: 3031629485 | 824 Pages | PDF EPUB (True) | 96 MB
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.