Unsolved Problems in Number Theory

  • Richard K. Guy

Part of the Problem Books in Mathematics book series (PBM, volume 1)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Richard K. Guy
    Pages 1-2
  3. Richard K. Guy
    Pages 3-43
  4. Richard K. Guy
    Pages 44-104
  5. Richard K. Guy
    Pages 105-138
  6. Richard K. Guy
    Pages 139-198
  7. Richard K. Guy
    Pages 199-239
  8. Richard K. Guy
    Pages 240-267
  9. Back Matter
    Pages 268-287

About this book

Introduction

To many laymen, mathematicians appear to be problem solvers, people who do "hard sums". Even inside the profession we dassify ouselves as either theorists or problem solvers. Mathematics is kept alive, much more than by the activities of either dass, by the appearance of a succession of unsolved problems, both from within mathematics itself and from the increasing number of disciplines where it is applied. Mathematics often owes more to those who ask questions than to those who answer them. The solution of a problem may stifte interest in the area around it. But "Fermat 's Last Theorem", because it is not yet a theorem, has generated a great deal of "good" mathematics, whether goodness is judged by beauty, by depth or by applicability. To pose good unsolved problems is a difficult art. The balance between triviality and hopeless unsolvability is delicate. There are many simply stated problems which experts tell us are unlikely to be solved in the next generation. But we have seen the Four Color Conjecture settled, even if we don't live long enough to learn the status of the Riemann and Goldbach hypotheses, of twin primes or Mersenne primes, or of odd perfect numbers. On the other hand, "unsolved" problems may not be unsolved at all, or than was at first thought.

Keywords

Zahlentheorie arithmetic Mersenne prime number theory prime number

Authors and affiliations

  • Richard K. Guy
    • 1
  1. 1.Department of Mathematics and StatisticsThe University of CalgaryCalgaryCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4899-3585-4
  • Copyright Information Springer-Verlag New York 1994
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4899-3587-8
  • Online ISBN 978-1-4899-3585-4
  • Series Print ISSN 0941-3502
  • About this book