Daily Archives: March 6, 2015

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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