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Complete residue system of a[i]b[j]

Source: Kürschak 2010, problem 3

July 8, 2014
number theory unsolvednumber theory

Problem Statement

For what positive integers nn and kk do there exits integers a1,a2,…,ana_1,a_2,\dots,a_n and b1,b2,…,bkb_1,b_2,\dots,b_k such that the products aibja_ib_j (1≤i≤n,1≤j≤k1\le i\le n,1\le j\le k) give pairwise different residues modulo nknk?
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