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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 11 to 19991999 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?