Unsolved Problems in Number Theory contains discussions of hundreds of open questions, organized into 185 different topics. They represent numerous aspects of number theory and are organized into six 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, not only extensive new material has been added, but corrections and additions have been included throughout the book.
It's difficult to keep track of the important and/or interesting unsolved problems in any field, but number theory is particularly broad and deep. Richard Guy attempts to do the impossible and cover the unsolved problems of number theory, and he does it so well that this was *the* book I carried with me constantly as an undergraduate. Highly recommended for any person at any level looking for topics to think and wonder about. And, just maybe, solve!