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Number theory, the branch of mathematics which studies the properties of the integers, is a repository of interesting and quite varied problems, sometimes impossibly difficult ones. The authors have gathered together a collection of problems from various topics in number theory that they find beautiful, intriguing, and from a certain point of view instructive. In addition to revealing the beauty of the problems themselves, they have tried to give glimpses into deeper, related mathematics. The book presents problems whose solutions can be obtained using elementary methods. No prior knowledge of number theory is assumed.