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partition set 1,2,...,1998 into 3 sets with sums 2000, 3999 and 5998

Source: North Macedonian Mathematical Olympiad 1998 p2

February 12, 2020
setpartitionSumcombinatoricsalgebra

Problem Statement

Prove that the numbers 1,2,...,19981,2,...,1998 cannot be separated into three classes whose sums of elements are divisible by 2000,39992000,3999, and 59985998, respectively.