An introduction to Diophantine equations: a problem-based approach

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." Provides reader with the main elementary methods necessary in solving Diophantine equations Approaches Diophantine equations from a problem-solving standpoint, including some original exercises and solutions Covers classical Diophantine equations, including linear, Pythagorean and higher degree equations, as well as exponential Diophantine equations INDICE: Preface.- Part 1: Diophantine Equations.- Elementary Methods for Solving Diophantine Equations.- Some Classical Diophantine Equation.- Pell’s-Type Equations.- Part 2: Solutions to Exercises and Problems.- Elementary Methods for Solving Diophantine Equations.- Some Classical Diophantine Equation.- Pell’s-Type Equations.- References.- Index.

• ISBN: 978-0-8176-4548-9
• Editorial: Birkhaüser
• Encuadernacion: Cartoné
• Páginas: 344
• Fecha Publicación: 29/09/2010
• Nº Volúmenes: 1
• Idioma: Inglés