# 2012 USAMO Problems/Problem 3

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## Problem

Determine which integers $n > 1$ have the property that there exists an infinite sequence $a_1$, $a_2$, $a_3$, $\dots$ of nonzero integers such that the equality $\[a_k + 2a_{2k} + \dots + na_{nk} = 0\]$ holds for every positive integer $k$.