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© 2015

Quadratic Diophantine Equations

Benefits

  • Includes both theoretical and computational examples

  • Explores new computational techniques for quadratic diophantine equations

  • Techniques presented will shed light on important open problems

Textbook

Part of the Developments in Mathematics book series (DEVM, volume 40)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Titu Andreescu, Dorin Andrica
    Pages 1-8
  3. Titu Andreescu, Dorin Andrica
    Pages 31-53
  4. Titu Andreescu, Dorin Andrica
    Pages 55-105
  5. Titu Andreescu, Dorin Andrica
    Pages 107-143
  6. Titu Andreescu, Dorin Andrica
    Pages 145-167
  7. Titu Andreescu, Dorin Andrica
    Pages 169-199
  8. Back Matter
    Pages 201-211

About this book

Introduction

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.

Keywords

Pell's equation algebra diophantine equations number theory

Authors and affiliations

  1. 1.School of Natural Sciences and MathematicsUniversity of Texas at DallasRichardsonUSA
  2. 2.Faculty of Mathematics & Computer Science"Babeş-Bolyai" UniversityCluj-NapocaRomania

Bibliographic information

  • Book Title Quadratic Diophantine Equations
  • Authors Titu Andreescu
    Dorin Andrica
  • Series Title Developments in Mathematics
  • Series Abbreviated Title DEVM
  • DOI https://doi.org/10.1007/978-0-387-54109-9
  • Copyright Information Springer Science+Business Media New York 2015
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-0-387-35156-8
  • Softcover ISBN 978-1-4939-3880-3
  • eBook ISBN 978-0-387-54109-9
  • Series ISSN 1389-2177
  • Series E-ISSN 2197-795X
  • Edition Number 1
  • Number of Pages XVIII, 211
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Number Theory
    Algebra
  • Buy this book on publisher's site
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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)