# 2015-1 Equal sums

Let $$A$$ be a set of $$n\ge 2$$ odd integers. Prove that there exist two distinct subsets $$X$$, $$Y$$ of $$A$$ such that $\sum_{x\in X} x\equiv\sum_{y\in Y}y \pmod{2^n}.$

Remark (added March 3): n is an integer greater than or equal to 2 and A is a set of n odd integers.

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