Imo Problems, Theorems, And Methods: Number Theory (Mathematical Olympiad Series)

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 the number theory volume, the IMO number theory problems are organized into three chapters: "Divisibility of Integers," "Modular Arithmetic," and "Indeterminate Equations." Each chapter begins with an introduction to the relevant foundational knowledge and methods, followed by a reclassification and reorganization of past IMO problems. Multiple elegant solutions are provided for some of the problems, along with a statistical analysis of their difficulty. The book concludes with a record of past IMO participation and award information, as well as an index of number theory problems, facilitating further study and convenient reference. This series is suitable for researchers in mathematical competitions, mathematics educators, and contestants.

Gengyu Zhang, graduated from School of Mathematical Sciences of Peking University as an undergraduate and Columbia University as a graduate. During high school he won two gold medals in Chinese Mathematical Olympiad (CMO). After graduation, he has always maintained his interest and passion in mathematical competitions, conducted research on formulating and solving mathematical problems, and participated in a wide range of mathematical education activities in primary and secondary schools.

Bin Xiong is a professor and doctoral supervisor at the School of Mathematical Sciences, East China Normal University, director of the Shanghai Key Laboratory of Core Mathematics and Practice, and director of the International Mathematical Olympiad Research Center. He is an expert with special allowance from the State Council, awarded the Shanghai May Day Labor Medal, and recognized as a model teacher and educator in Shanghai. More than 100 papers have been published both domestically and internationally, and over 150 books have been edited and co-authored. He served as the leader and head coach of the Chinese team at the International Mathematical Olympiad more than 10 times and received the Paul Erdos Award for International Mathematics in 2018.