A proof of snevily’s conjecture

Abstract

We prove Snevily’s conjecture, which states that for any positive integer k and any two k-element subsets {a₁, …, a_k} and {b₁, …, b_k} of a finite abelian group of odd order there exists a permutation π ∈ S_k such that all sums a_i + b_π(i) (i ∈ [1, k]) are pairwise distinct.