KURSCHAK 2010 Problem 3

For what positive integers $n$ and $k$ do there exits integers $a_1,a_2,\dots,a_n$ and $b_1,b_2,\dots,b_k$ such that the products $a_ib_j$ ( $1\le i\le n,1\le j\le k$ ) give pairwise different residues modulo $nk$ ?