Elements of the theory of divisibility in the solution Olympiad tasks

The article discusses the importance of studying the basics of the elements of the theory of divisibility. Knowledge of the elements of the theory of divisibility is needed by students of any age when solving Olympiad problems. Various ways of solving divisibility problems for preparation for the Olympiads are being analyzed. Examples of Olympiad problems with solutions on the topics "Signs of divisibility", "Divisibility with remainder", "Prime and composite numbers", etc. are given. Based on the analysis of methodological and mathematical literature, observation of students in solving Olympiad problems, the authors concluded that solving Olympiad problems requires more strenuous work of decision makers, sorting through a variety of solutions, checking "themselves" in the ability to look for non-standard solutions, competently argue analyses and conclusions.