Olympiad Number Theory Through Challenging Problems (pdf)
Third Edition published December 18th, 2016 with the story behind the text.
An 120 page introductory Olympiad Number Theory book I wrote for anyone with a passion for number theory and problem solving published on the Art of Problem Solving website. Each section begins by introducing a main concept or idea, and then contains many engaging and challenging problems. My goal for the text was to show how several problem solving skills–experimenting with small cases, simplification, and pattern finding–can be used to tackle a wide variety of Olympiad Number Theory problems. There are five chapters on Divisibility, Modular Arithmetic, p-adic valuation, Diophantine Equations, and Problem Solving Strategies.