Suppose G is a finite abelian group and S is a sequence of elements in G. For any element g of G, let Ng(S) denote the number of subsequences of S with sum g. The purpose of this paper is to investigate the lower bound for Ng(S). In particular, we prove that either Ng(S) = 0 or Ng(S) ≥ 2 |S|−D(G)+1, where D(G) is the smallest positive integer l such that… (More)