  Let $n$ be a positive integer and let $S$ be a sequence of $n$ integers in
the interval $[0,n-1]$. If there is an $r$ such that any nonempty subsequence
with sum $\equiv 0$ $\pmod n$ has length $=r,$ then $S$ has at most two
distinct values. This proves a conjecture of R. L. Graham. A previous result of
P. Erd\H{o}s and E. Szemer\'edi shows the validity of this conjecture if $n$ is
a large prime number.
