An Introduction to Diophantine Equations [electronic resource] : A Problem-Based Approach / by Titu Andreescu, Dorin Andrica, Ion Cucurezeanu.
Contributor(s): Andrica, Dorin [author.] | Cucurezeanu, Ion [author.] | SpringerLink (Online service)Material type: TextPublisher: Boston : Birkhäuser Boston, 2010Description: XI, 345p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780817645496Subject(s): Mathematics | Algebra | Number theory | Mathematics | Number Theory | AlgebraAdditional physical formats: Printed edition:: No titleDDC classification: 512.7 LOC classification: QA241-247.5Online resources: Click here to access online
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Diophantine Equations -- Elementary Methods for Solving Diophantine Equations -- Some Classical Diophantine Equations -- Pell-Type Equations -- Some Advanced Methods for Solving Diophantine Equations -- Solutions to Exercises and Problems -- Solutions to Elementary Methods for Solving Diophantine Equations -- Solutions to Some Classical Diophantine Equations -- Solutions to Pell-Type Equations -- Solutions to Some Advanced Methods in Solving Diophantine Equations.
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.