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Solving the Pell Equation

  • Michael J. JacobsonJr.
  • Hugh C. Williams
Textbook

Part of the CMS Books in Mathematics book series (CMSBM)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Michael J. Jacobson Jr., Hugh C. Williams
    Pages 1-17
  3. Michael J. Jacobson Jr., Hugh C. Williams
    Pages 19-41
  4. Michael J. Jacobson Jr., Hugh C. Williams
    Pages 43-73
  5. Michael J. Jacobson Jr., Hugh C. Williams
    Pages 75-96
  6. Michael J. Jacobson Jr., Hugh C. Williams
    Pages 97-124
  7. Michael J. Jacobson Jr., Hugh C. Williams
    Pages 125-152
  8. Michael J. Jacobson Jr., Hugh C. Williams
    Pages 153-184
  9. Michael J. Jacobson Jr., Hugh C. Williams
    Pages 185-207
  10. Michael J. Jacobson Jr., Hugh C. Williams
    Pages 209-235
  11. Michael J. Jacobson Jr., Hugh C. Williams
    Pages 237-264
  12. Michael J. Jacobson Jr., Hugh C. Williams
    Pages 265-283
  13. Michael J. Jacobson Jr., Hugh C. Williams
    Pages 285-305
  14. Michael J. Jacobson Jr., Hugh C. Williams
    Pages 307-352
  15. Michael J. Jacobson Jr., Hugh C. Williams
    Pages 353-386
  16. Michael J. Jacobson Jr., Hugh C. Williams
    Pages 387-404
  17. Michael J. Jacobson Jr., Hugh C. Williams
    Pages 405-421
  18. Michael J. Jacobson Jr., Hugh C. Williams
    Pages 423-437
  19. Back Matter
    Pages 439-495

About this book

Introduction

Pell's equation is a very simple, yet fundamental Diophantine equation which is believed to have been known to mathematicians for over 2000 years. Because of its popularity, the Pell equation is often discussed in textbooks and recreational books concerning elementary number theory, but usually not in much depth. This book provides a modern and deeper approach to the problem of solving the Pell equation. The main component of this will be computational techniques, but in the process of deriving these it will be necessary to develop the corresponding theory.

 

One objective of this book is to provide a less intimidating introduction for senior undergraduates and others with the same level of preparedness to the delights of algebraic number theory through the medium of a mathematical object that has fascinated people since the time of Archimedes. To achieve this, this work is made accessible to anyone with some knowledge of elementary number theory and abstract algebra. Many references and notes are provided for those who wish to follow up on various topics, and the authors also describe some rather surprising applications to cryptography.

 

The intended audience is number theorists, both professional and amateur, and students, but we wish to emphasize that this is not intended to be a textbook; its focus is much too narrow for that. It could, however be used as supplementary reading for students enrolled in a second course in number theory.

Keywords

algebra algebraic number theory cryptography diophantine equation number theory

Authors and affiliations

  • Michael J. JacobsonJr.
    • 1
  • Hugh C. Williams
    • 2
  1. 1.Department of Computer ScienceUniversity of CalgaryCalgaryCanada
  2. 2.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada

Bibliographic information