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 ≡ 0 (mod 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. Erdős and E. Szemerédi shows the validity of this conjecture if n is a large prime number.
