  A subset $X$ of an abelian $G$ is said to be {\em complete} if every element
of the subgroup generated by $X$ can be expressed as a nonempty sum of distinct
elements from $X$.
  Let $A\subset \Z_n$ be such that all the elements of $A$ are coprime with
$n$. Solving a conjecture of Erd\H{o}s and Heilbronn, Olson proved that
  $A$ is complete if $n$ is a prime and if $|A|>2\sqrt{n}.$
  Recently Vu proved that there is an absolute constant $c$, such that for an
arbitrary large $n$, $A$ is complete if $|A|\ge c\sqrt{n},$ and conjectured
that 2 is essentially the right value of $c$. We show that $A$ is complete if
$|A|> 1+2\sqrt{n-4}$, thus proving the last conjecture.
