On complete subsets of the cyclic group

A subset X of an abelian G is said to be complete if every element of the subgroup generated by X can be expressed as a nonempty sum of distinct elements from X . Let A ⊂ Zn be such that all the elements of A are coprime with n. Solving a conjecture of Erdős and Heilbronn, Olson proved that A is complete if n is a prime and if |A| > 2√n. Recently Vu proved that there is an absolute constant c, such that for an arbitrary large n, A is complete if |A| ≥ c√n, and conjectured that 2 is essentially the right value of c. We show that A is complete if |A| > 1 + 2 √ n− 4, thus proving the last conjecture.