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Unsolved Problems in Number Theory

  • Textbook
  • © 1981

Overview

Authors:
  1. Richard K. Guy

    1. Department of Mathematics and Statistics, The University of Calgary, Calgary, Canada

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

Part of the book sub series: Unsolved Problems in Intuitive Mathematics (1605)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Introduction

    • Richard K. Guy
    Pages 1-2

  3. Prime Numbers

    • Richard K. Guy
    Pages 3-24

  4. Divisibility

    • Richard K. Guy
    Pages 25-57

  5. Additive Number Theory

    • Richard K. Guy
    Pages 58-78

  6. Some Diophantine Equations

    • Richard K. Guy
    Pages 79-109

  7. Sequences of Integers

    • Richard K. Guy
    Pages 110-131

  8. None of the Above

    • Richard K. Guy
    Pages 132-148

  9. Back Matter

    Pages 149-161
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Keywords

About this book

To many laymen, mathematicians appear to be problem solvers, people who do "hard sums". Even inside the profession we dassify ourselves 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 in­ creasing number of disciplines where it is applied. Mathematics often owes more to those who ask questions than to those who answer them. The solu­ tion 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 byapplicability. 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 ifwe don't live long enough to leam the status of the Riemann and Goldbach hypotheses, of twin primes or Mersenne primes, or of odd perfeet numbers. On the other hand, "unsolved" problems may not be unsolved at all, or may be much more tractable than was at first thought.

Reviews

From the reviews of the third edition:

"This is the third edition of Richard Guy’s well-known problem book on number theory … . The earlier editions have served well in providing beginners as well as seasoned researchers in number theory with a good supply of problems. … many of the problems from earlier editions have been expanded with more up-to-date comments and remarks. … There is little doubt that a new generation of talented young mathematicians will make very good use of this book … ." (P. Shiu, The Mathematical Gazette, Vol. 89 (516), 2005)

"The earlier editions of this book are among the most-opened books on the shelves of many practicing number theorists. The descriptions of state-of-the-art results on every topic and the extensive bibliographies in each section provide valuable ports of entry to the vast literature. A new and promising addition to this third edition is the inclusion of frequent references to entries in the Online encyclopedia of integer sequences at the end of each topic." (Greg Martin, Mathematical Reviews, Issue 2005 h)

Authors and Affiliations

  • Department of Mathematics and Statistics, The University of Calgary, Calgary, Canada

    Richard K. Guy

Bibliographic Information

  • Book Title: Unsolved Problems in Number Theory

  • Authors: Richard K. Guy

  • Series Title: Problem Books in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4757-1738-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1981

  • eBook ISBN: 978-1-4757-1738-9Published: 29 June 2013

  • Series ISSN: 0941-3502

  • Series E-ISSN: 2197-8506

  • Edition Number: 1

  • Number of Pages: XVIII, 161

  • Number of Illustrations: 9 b/w illustrations

  • Topics: Number Theory, Discrete Mathematics

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