sum of proper fractions (VI Soros Olympiad 1990-00 R1 8.6)
Source:
May 27, 2024
algebranumber theory
Problem Statement
Two players take turns writing down all proper non-decreasing fractions with denominators from to and at the same time writing a "" sign before each fraction. After all such fractions are written out, their sum is found. If this amount is an integer number, then the one who made the entry last wins, otherwise his opponent wins. Who will be able to secure a win?