Pell’s Equation

  • Edward J. Barbeau

Part of the Problem Books in Mathematics book series (PBM)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Edward J. Barbeau
    Pages 1-15
  3. Edward J. Barbeau
    Pages 32-42
  4. Edward J. Barbeau
    Pages 43-54
  5. Edward J. Barbeau
    Pages 55-80
  6. Edward J. Barbeau
    Pages 81-91
  7. Edward J. Barbeau
    Pages 92-112
  8. Edward J. Barbeau
    Pages 113-125
  9. Edward J. Barbeau
    Pages 126-137
  10. Back Matter
    Pages 139-213

About this book

Introduction

 Pell's equation is an important topic of algebraic number theory that involves quadratic forms and the structure of rings of integers in algebraic number fields. The history of this equation is long and circuitous, and involved a number of different approaches before a definitive theory was found. There were partial patterns and quite effective methods of finding solutions, but a complete theory did not emerge until the end of the eighteenth century.

The topic is motivated and developed through sections of exercises which allow the student to recreate known theory and provide a focus for their algebraic practice. There are also several explorations that encourage the reader to embark on their own research. Some of these are numerical and often require the use of a calculator or computer. Others introduce relevant theory that can be followed up on elsewhere, or suggest problems that the reader may wish to pursue. A high school background in mathematics is all that is needed to get into this book, and teachers and others interested in mathematics who do not have a background in advanced mathematics may find that it is a suitable vehicle for keeping up an independent interest in the subject.

Edward Barbeau is Professor of Mathematics at the University of Toronto. He has published a number of books directed to students of mathematics and their teachers, including Polynomials (Springer 1989), Power Play (MAA 1997), Fallacies, Flaws and Flimflam (MAA 1999) and After Math (Wall & Emerson, Toronto 1995).

Keywords

algebra algebraic number field algebraic number theory diophantine equation number theory quadratic form

Authors and affiliations

  • Edward J. Barbeau
    • 1
  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada

Bibliographic information

  • DOI https://doi.org/10.1007/b97610
  • Copyright Information Springer Science+Business Media New York 2003
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-3040-8
  • Online ISBN 978-0-387-22602-6
  • Series Print ISSN 0941-3502
  • About this book
Industry Sectors
Telecommunications
Aerospace
Pharma