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  • Unsolved Problems in Number Theory (Problem Books in Mathematics, 1)

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Unsolved Problems in Number Theory (Problem Books in Mathematics, 1)

by Richard Guy (Author) Format: Hardcover
4.8 out of 5 stars (11)
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Mathematics is kept alive by the appearance of new unsolved problems, problems posed from within mathematics itself, and also from the increasing number of disciplines where mathematics is applied. This book provides a steady supply of easily understood, if not easily solved, problems which can be considered in varying depths by mathematicians at all levels of mathematical maturity.

For this new edition, the author has included new problems on symmetric and asymmetric primes, sums of higher powers, Diophantine m-tuples, and Conway's RATS and palindromes. The author has also included a useful new feature at the end of several of the sections: lists of references to OEIS, Neil Sloane's Online Encyclopedia of Integer Sequences.

About the first Edition:

"...many talented young mathematicians will write their first papers starting out from problems found in this book." András Sárközi, MathSciNet

Read more
Previous slide of product details
  1. ISBN-10
    0387208607
  2. ISBN-13
    978-0387208602
  3. Edition
    3rd
  4. Publisher
    Springer
  5. Publication date
    July 13, 2004
  6. Part of series
    Problem Books in Mathematics
  7. Language
    English
  8. Dimensions
    6.5 x 0.5 x 9.5 inches
  9. Print length
    456 pages
Next slide of product details

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Editorial Reviews

Review

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)

From the Back Cover

Mathematics is kept alive by the appearance of new unsolved problems, problems posed from within mathematics itself, and also from the increasing number of disciplines where mathematics is applied. This book provides a steady supply of easily understood, if not easily solved, problems which can be considered in varying depths by mathematicians at all levels of mathematical maturity.

For this new edition, the author has included new problems on symmetric and asymmetric primes, sums of higher powers, Diophantine m-tuples, and Conway’s RATS and palindromes. The author has also included a useful new feature at the end of several of the sections: lists of references to OEIS, Neil Sloane’s Online Encyclopedia of Integer Sequences.

About the First Edition:

"…many talented young mathematicians will write their first papers starting out from problems found in this book."

- András Sárközi, MathSciNet

Product details

  • Publisher ‏ : ‎ Springer
  • Publication date ‏ : ‎ July 13, 2004
  • Edition ‏ : ‎ 3rd
  • Language ‏ : ‎ English
  • Print length ‏ : ‎ 456 pages
  • ISBN-10 ‏ : ‎ 0387208607
  • ISBN-13 ‏ : ‎ 978-0387208602
  • Item Weight ‏ : ‎ 1.75 pounds
  • Dimensions ‏ : ‎ 6.5 x 0.5 x 9.5 inches
  • Part of series ‏ : ‎ Problem Books in Mathematics
  • Best Sellers Rank: #1,437,083 in Books (See Top 100 in Books)
  • Customer Reviews:
    4.8 out of 5 stars (11)

About the author

Follow authors to get new release updates, plus improved recommendations.
Richard K. Guy

Richard K. Guy

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Customer reviews

4.8 out of 5 stars
11 global ratings

Top reviews from the United States

  • Jamie Simpson
    5 out of 5 stars
    Five Stars
    Reviewed in the United States on July 20, 2016
    Format: Paperback
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    This is the best collection of unsolved problems in number theory ever published.

    One person found this helpful
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  • Kindle Customer
    4 out of 5 stars
    Interesting Book
    Reviewed in the United States on August 18, 2024
    Format: Paperback
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    Full content visible, double tap to read brief content.

    This is a very interesting book for people who like math. Number theory is a good subject for non-techies.

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  • Greg C
    4 out of 5 stars
    Fulfills what was expected of it
    Reviewed in the United States on September 11, 2011
    Format: Hardcover
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    Full content visible, double tap to read brief content.

    Contains a surprising number of typographical errors. Good compilation of many, many extremely difficult problems, but not a textbook or learning resource by any means.

    4 people found this helpful
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Top reviews from other countries

  • Willy Van den Driessche
    5 out of 5 stars
    Only for number theory freaks
    Reviewed in France on October 7, 2010
    Format: Hardcover
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    Full content visible, double tap to read brief content.

    This is not a normal textbook. Although it has a substantial number of pages, it is little more than an enumeration of mathematical conjectures that are waiting for a solution. All of them are placed into a very brief context. Some of these are esoteric (like palindromic primes) but I personally find a lot of them interesting. For me as an amateur the nice thing is that you have some certitude that the problem you pick from this book has not long been solved.

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