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existence of a subset with sum divisible by n

Source: Indonesia TST 2016 Round 3

March 24, 2024
number theorySetsabstract algebra

Problem Statement

Let kk and nn be positive integers. Determine the smallest integer N≥kN \ge k such that the following holds: If a set of NN integers contains a complete residue modulo kk, then it has a non-empty subset whose sum of elements is divisible by nn.
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