SOLVING OLYMPIAD PROBLEMS USING INTEGER AND FRACTIONAL PARTS: A PEDAGOGICAL APPROACH

Abstract

This article presents a pedagogical framework for solving mathematical Olympiad problems using the integer part ([x], ant’ye) and fractional part ({x}, mantissa) of real numbers. Through detailed solutions to problems from competitions such as Yekaterinburg (2001–2002), SPbGU ITMO (2011–2012), and IMO (1979), we demonstrate techniques involving arithmetic roots, equivalent inequalities, and functional identities. These methods foster creative thinking and analytical skills, making them valuable for mathematics education. The article offers educators and students practical strategies for tackling nonroutine problems, enhancing preparation for mathematical competitions. By emphasizing clarity and pedagogical insights, we aim to inspire innovative teaching and learning practices in competitive mathematics.