We prove that for every odd prime p, every k ≤ p and every two subsets A = {a1, . . . , ak} and B = {b1, . . . , bk} of cardinality k each of Zp, there is a permutation π ∈ Sk such that the sums ai + bπ(i) (in Zp) are pairwise distinct. This partially settles a question of Snevily. The proof is algebraic, and implies several related results as well.
