Mathematics: Olympiad Problems: Grades 5-7

This manual discusses the main methods and techniques for solving Olympiad problems of varying difficulty levels for students in grades 5-7. The manual contains 750 problems, divided into 50 sets for each grade. Each set includes 5 problems on various topics. The problems presented in the book are dedicated to classic themes such as divisibility and remainders, invariants, Diophantine equations, the Dirichlet principle, solving equations in integers, graphing functions, etc. Answers and hints are provided for all problems, and solutions are given for the most difficult ones. Most of the problems are original. The concluding part of the book presents engaging creative problems related to numbers and numerical patterns, which generate increased interest not only among students but also among teachers. The manual is aimed at students in grades 5-7 preparing for Olympiads of various levels, as well as math teachers, students of pedagogical universities, and tutors.