Overview

This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.

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9781493938803

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Diophantine analysis aims to solve equations (usually polynomial) in integers (or rationals). ... this work settles the classical foundation, then develops state-of-the-art issues, especially concerning computation. ... Summing Up: Recommended. Lower-division undergraduates through professionals/practitioners. (D. V. Feldman, Choice, Vol. 53 (9), May, 2016) The primary focus of this book under review is the integer solutions of Pell equations, their generalisations and related diophantine equations, along with applications of these equations. ... The book is suitable for readers from the level of a motivated undergraduate upwards, who are interested in the classical techniques for solving such equations. ... There is also an extensive bibliography. (Paul M. Voutier, Mathematical Reviews, March, 2016)

Diophantine analysis aims to solve equations (usually polynomial) in integers (or rationals). ... this work settles the classical foundation, then develops state-of-the-art issues, especially concerning computation. ... Summing Up: Recommended. Lower-division undergraduates through professionals/practitioners. (D. V. Feldman, Choice, Vol. 53 (9), May, 2016) The primary focus of this book under review is the integer solutions of Pell equations, their generalisations and related diophantine equations, along with applications of these equations. ... The book is suitable for readers from the level of a motivated undergraduate upwards, who are interested in the classical techniques for solving such equations. ... There is also an extensive bibliography. (Paul M. Voutier, Mathematical Reviews, March, 2016)

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