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Quadratic Diophantine Equations

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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.

Authors: Andreescu Titu, Andrica Dorin
Publisher: SPRINGER
Pages: 229
ISBN: 9781493938803
Cover: Hardback
Edition Number: 1
Release Year: 2015

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.

Dr. Titu Andreescu is an Associate Professor at the University of Texas at Dallas in the Science and Mathematics Education department.

Kathy Cordeiro, MBA, is a leading developer of education initiatives for business and academia. She founded Eudaimonia Academy, where she coached mathematics teams and worked with highly and profoundly gifted students.

Alina Andreescu, MA, is the co-founder and Operations Director of AwesomeMath and founder of XYZ Press. She fosters an international community of staff, students, and instructors that values critical thinking, creativity, passionate problem solving, and lifetime mathematical learning.

Dorin Andrica is a Professor of Mathematics at the Babes-Bolyai University of Cluj Napoca, Romania. He has obtained a PhD in Pure Mathematics in 1992 with a thesis on critical point theory with applications to the geometry of differentiable submanifolds. His interests include differential topology (critical point theory with applications, Morse theory with applications), differential geometry,  geometry, Lie groups and Lie algebras with applications in geometric mechanics, number theory, discrete mathematics, and mathematics for competitions. Dorin has co-authored Springer textbooks on various topics in mathematics, as well as problem books for olympiad training. 

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