The problems in the International Mathematical Olympiad (IMO) are not only novel and interesting but also deeply rooted in profound mathematical context. The team at the International Mathematical Olympiad Research Center at East China Normal University has compiled and studied problems from past IMOs, dividing them into four volumes based on the mathematical fields involved: algebra, geometry, number theory, and combinatorics.In this book, we categorize IMO number theory problems into three major classes: divisibility of integers, modular arithmetic, and indeterminate equations. We first describe the origin and development of IMOs from the aspects of teams, prizes and problems, and compile the characteristics and trends of IMO number theory problems.In each chapter, we introduce the relevant basic knowledge and methods with some typical examples, then classify the IMO problems according to the knowledge and methods involved. For some problems, we provide various solutions. At last, we statistically analyze the difficulty and scoring situation of these IMO problems.