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There exists a partition of the set

Source: Moldova TST 2002 - E1 - P2

January 8, 2012
combinatorics unsolvedcombinatorics

Problem Statement

Prove that there exists a partition of the set A={13,23,…,20003}A = \{1^3, 2^3, \ldots , 2000^3\} into 1919 nonempty subsets such that the sum of elements of each subset is divisible by 200122001^2.
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