Number Theory: A Lively Introduction with Proofs, Applications, and Stories by Erica Flapan, James Pommersheim, Tim Marks (Hardback, 2010)
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A unique feature of the book is that every chapter includes a math myth, a fictional story that introduces an important number theory topic in a friendly, inviting manner. Many of the exercise sets include in-depth explorations, in which a series of exercises develop a topic that is related to the material in the section.