Problem

Source: 2012 USAMO problem #3

Tags: function, modular arithmetic, floor function, AMC, USA(J)MO, USAMO



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