An Introduction to Diophantine Equations: A Problem-Based Approach - Hardcover

Andreescu, Titu; Andrica, Dorin; Cucurezeanu, Ion

Hardcover

ISBN 10: 0817645489 ISBN 13: 9780817645489

Verlag: Birkhäuser, 2010

Inhaltsangabe

This book is an introduction to the study of Diophantine equations. The book, organized in two parts, introduces the reader to the main elementary methods necessary in solving Diophantine equations, presents some classical Diophantine equations, and contains complete solutions to all of the exercises. The book is intended for undergraduates, high school students and their teachers, mathematics contests participants (including Olympiad and Putnam competitors), as well as any person interested in essential mathematics. This work uniquely presents unconventional and non-routine examples, ideas, and techniques.

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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.

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 2010
• Sprache: Englisch
• ISBN 10: 0817645489
• ISBN 13: 9780817645489
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 356
• Kontakt zum Hersteller: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Deutschland