Amazon.com Book Description (ISBN 0387942890, Hardcover)

This book contains discussions of hundreds of open questions in number theory, organized into 185 different topics. They represent numerous aspects of number theory and are organized into six categories: prime numbers, divisibility, additive number theory, Diophantine equations, sequences of integers, and miscellaneous. To prevent repetition of earlier efforts or duplication of previously known results, an extensive and up-to-date collection of references follows each problem. In the second edition, extensive new material has been added, and corrections have been included throughout the book. This volume is an invaluable supplement to any course in number theory.

Amazon.com Product Description (ISBN 0387208607, Hardcover)

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