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This book reveiws the last two decades of computational techniques and progress in the classical theory of quadratic diophantine equations. Presents important quadratic diophantine equations and applications, and includes excellent examples and open problems.

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This text 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. The presentation features two basic methods to investigate and motivate the study of quadratic diophantine equations: the theories of continued fractions and quadratic fields. It also discusses Pell´s equation and its generalizations, and presents some important quadratic diophantine equations and applications. The inclusion of examples makes this book useful for both research and classroom settings.

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Why Quadratic Diophantine Equations?.- Continued Fractions, Diophantine Approximation and Quadratic Rings.- Pell´s Equation.- General Pell´s Equation.- Equations Reducible to Pell´s Type Equations.- Diophantine Representations of Some Sequences.- Other Applications.

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"The book under review is an excellent book on the interesting subject of quadratic Diophantine equations. It is well written, well organized, and contains a wealth of material that one does not expect to find in a book of its size, with full proofs of scores of theorems. ... This reviewer does not know any book that covers similar material, and sees it as a very valuable and much needed addition to the literature on number theory." (Mowaffaq Hajja, zbMATH 1376.11001, 2018)

"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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