An Introduction to Diophantine Equations: A Problem-Based Approach, 2010, 356pages, Titu Andreescu, Dorin Andrica, Ion Cucurezeanu, 0817645497,9780817645496, Springer Science & Business Media, 2010

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This problem-solving book is an introduction to the study of Diophantine equations, a class ofequations in which only integer solutions are allowed. The material is organized in two parts: Part Iintroduces the reader to elementary methods necessary in solving Diophantine equations, such asthe decomposition method, inequalities, the parametric method, modular arithmetic, mathematicalinduction, Fermat's method of infinite descent, and the method of quadratic fields; Part II containscomplete solutions to all exercises in Part I. The presentation features some classical Diophantineequations, including linear, Pythagorean, and some higher degree equations, as well asexponential Diophantine equations. Many of the selected exercises and problems are original or arepresented with original solutions. An Introduction to Diophantine Equations: A Problem-BasedApproach is intended for undergraduates, advanced high school students and teachers,mathematical contest participants — including Olympiad and Putnam competitors — as well asreaders interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques.

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