Synopses & Reviews
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
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)
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)
Synopsis
Second edition sold 2241 copies in N.A. and 1600 ROW.
New edition contains 50 percent new material.
Synopsis
From reviews of the first edition:
...many talented young mathematicians will write their first papers starting out from problems found in this book. -Mathematical Reviews
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.
Synopsis
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
Synopsis
Mathematics is kept alive by the appearance of new, unsolved problems. This book provides a steady supply of easily understood, if not easily solved, problems that can be considered in varying depths by mathematicians at all levels of mathematical maturity. This new edition features lists of references to OEIS, Neal Sloane's Online Encyclopedia of Integer Sequences, at the end of several of the sections.
Table of Contents
Preface to the First Edition
Preface to the Second Edition
Preface to the Third Edition
Glossary of Symbols
A. Prime Numbers.
A1. Prime values of quadratic functions.
A2. Primes connected with factorials.
A3. Mersenne primes. Repunits. Fermat numbers. Primes of shape k · 2n + 1.
A4. The prime number race.
A5. Arithmetic progressions of primes.
A6. Consecutive primes in A.P.
A7. Cunningham chains.
A8. Gaps between primes. Twin primes.
A9. Patterns of primes.
A10. Gilbreath's conjecture.
A11. Increasing and decreasing gaps.
A12. Pseudoprimes. Euler pseudoprimes. Strong pseudoprimes.
A13. Carmichael numbers.
A14. "Good" primes and the prime number graph.
A15. Congruent products of consecutive numbers.
A16. Gaussian primes. Eisenstein-Jacobi primes.
A17. Formulas for primes.
A18. The Erd½os-Selfridge classi.cation of primes.