Let G be an additive finite abelian group of order n, and let S be a
sequence of n+k elements in G, where kβ₯1. Suppose that S contains
t distinct elements. Let βnβ(S) denote the set that consists of all
elements in G which can be expressed as the sum over a subsequence of length
n. In this paper we prove that, either 0ββnβ(S) or β£βnβ(S)β£β₯k+tβ1. This confirms a conjecture by Y.O. Hamidoune in 2000