A subset X of an abelian G is said to be complete if every element of G can be expressed as a nonempty sum of distinct elements from X. Let A@?Z"n be such that all the elements of A are coprime with n. Solving a conjecture of Erdos and Heilbronn, Olson proved that A is complete if n is a prime and if |A|>2n. Recently Vu proved that there is an absolute constant c, such that for an arbitrary large n, A is complete if |A|>=cn, and conjectured that 2 is essentially the right value of c. We show that A is complete if |A|>1+2n-4, thus proving the last conjecture.
['Yahya Ould Hamidoune', 'Anna S. Lladó', 'Oriol Serra']
On complete subsets of the cyclic group