Elements of Number Theory

  • John Stillwell

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xii
  2. John Stillwell
    Pages 1-21
  3. John Stillwell
    Pages 22-42
  4. John Stillwell
    Pages 43-65
  5. John Stillwell
    Pages 66-75
  6. John Stillwell
    Pages 76-100
  7. John Stillwell
    Pages 101-116
  8. John Stillwell
    Pages 117-137
  9. John Stillwell
    Pages 138-157
  10. John Stillwell
    Pages 158-180
  11. John Stillwell
    Pages 181-195
  12. John Stillwell
    Pages 196-220
  13. John Stillwell
    Pages 221-238
  14. Back Matter
    Pages 239-254

About this book


 This book is a concise introduction to number theory and some related algebra, with an emphasis on solving equations in integers. Finding integer solutions led to two fundamental ideas of number theory in ancient times - the Euclidean algorithm and unique prime factorization - and in modern times to two fundamental ideas of algebra - rings and ideals.

The development of these ideas, and the transition from ancient to modern, is the main theme of the book. The historical development has been followed where it helps to motivate the introduction of new concepts, but modern proofs have been used where they are simpler, more natural, or more interesting. These include some that have not yet appeared in textbooks, such as a treatment of the Pell equation using Conway's theory of quadratic forms. Also, this is the only elementary number theory book that includes significant applications of ideal theory. It is clearly written, well illustrated, and supplied with carefully designed exercises, making it a pleasure to use as an undergraduate textbook or for independent study.

John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regarded books published by Springer-Verlag, including Mathematics and Its History (Second Edition 2001), Numbers and Geometry (1997) and Elements of Algebra (1994).


Euclidean algorithm number theory prime number

Authors and affiliations

  • John Stillwell
    • 1
  1. 1.Mathematics DepartmentUniversity of San FranciscoSan FranciscoUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag New York 2003
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-3066-8
  • Online ISBN 978-0-387-21735-2
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site