Shanks D. Solved and Unsolved Problems in Number Theory

Chelsea Pub. Co, 1978. - 255 pages.The investigation of three problems, that of perfect numbers, that of periodic decimals, and that of Pythagorean numbers has given rise to much of elementary number theory, and the author shows how each result gives rise to further results and conjectures. He treats not only results and theorems ("solved problems") but also questions that are still open and conjectures ("unsolved problems"), making this a most exciting and unusual treatment. The author, a past editor of Mathematics of Computation, presents research done in the fifteen years between the first and second editions, with emphasis on results that were achieved with the aid of computers. The volume includes a substantial Bibliography.