Overview
- Includes both theoretical and computational examples
- Explores new computational techniques for quadratic diophantine equations
- Techniques presented will shed light on important open problems
- Includes supplementary material: sn.pub/extras
Part of the book series: Developments in Mathematics (DEVM, volume 40)
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Table of contents (7 chapters)
Keywords
About this book
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.
Reviews
“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)
Authors and Affiliations
Bibliographic Information
Book Title: Quadratic Diophantine Equations
Authors: Titu Andreescu, Dorin Andrica
Series Title: Developments in Mathematics
DOI: https://doi.org/10.1007/978-0-387-54109-9
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2015
Hardcover ISBN: 978-0-387-35156-8Published: 30 June 2015
Softcover ISBN: 978-1-4939-3880-3Published: 09 October 2016
eBook ISBN: 978-0-387-54109-9Published: 29 June 2015
Series ISSN: 1389-2177
Series E-ISSN: 2197-795X
Edition Number: 1
Number of Pages: XVIII, 211
Topics: Number Theory, Algebra