# An Introduction to Diophantine Equations

## A Problem-Based Approach

• Titu Andreescu
• Dorin Andrica
• Ion Cucurezeanu
Book

1. Front Matter
Pages I-XI
2. ### Diophantine Equations

1. Front Matter
Pages 1-1
2. Titu Andreescu, Dorin Andrica, Ion Cucurezeanu
Pages 3-65
3. Titu Andreescu, Dorin Andrica, Ion Cucurezeanu
Pages 67-116
4. Titu Andreescu, Dorin Andrica, Ion Cucurezeanu
Pages 117-145
5. Titu Andreescu, Dorin Andrica, Ion Cucurezeanu
Pages 147-190
3. ### Solutions to Exercises and Problems

1. Front Matter
Pages 191-191
2. Titu Andreescu, Dorin Andrica, Ion Cucurezeanu
Pages 193-263
3. Titu Andreescu, Dorin Andrica, Ion Cucurezeanu
Pages 265-287
4. Titu Andreescu, Dorin Andrica, Ion Cucurezeanu
Pages 289-307
5. Titu Andreescu, Dorin Andrica, Ion Cucurezeanu
Pages 309-326
4. Back Matter
Pages 327-345

### Introduction

This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The material is organized in two parts: Part I introduces the reader to elementary methods necessary in solving Diophantine equations, such as the decomposition method, inequalities, the parametric method, modular arithmetic, mathematical induction, Fermat's method of infinite descent, and the method of quadratic fields; Part II contains complete solutions to all exercises in Part I. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions.

An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants — including Olympiad and Putnam competitors — as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques.

### Keywords

Fermat's method of infinite descent Gaussian integers Pell-type equations Pythagorean triples arithmetic boundary element method class diophantine equation equation history of mathematics mathematics number theory parametric method presentation techniques

#### Authors and affiliations

• Titu Andreescu
• 1
• Dorin Andrica
• 2
• Ion Cucurezeanu
• 3
1. 1.School of Natural Sciences and MathematiUniversity of Texas at DallasRichardsonUSA
2. 2.Faculty of Mathematics and Computer ScieBabeş-Bolyai UniversityCluj-NapocaRomania
3. 3.Faculty of Mathematics and Computer ScieOvidius University of ConstantaConstantaRomania

### Bibliographic information

• DOI https://doi.org/10.1007/978-0-8176-4549-6
• Publisher Name Birkhäuser Boston
• eBook Packages Mathematics and Statistics
• Print ISBN 978-0-8176-4548-9
• Online ISBN 978-0-8176-4549-6