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Exist subset with sum divisible by n

Source: China Second Round (A) 2013 Q4

May 15, 2016
number theory

Problem Statement

Let n,kn,k be integers greater than 11, n<2kn<2^k. Prove that there exist 2k2k integers none of which are divisible by nn, such that no matter how they are separated into two groups there exist some numbers all from the same group whose sum is divisible by nn.
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