THE NUMBER OF ZERO SUMS MODULO M IN A SEQUENCE OF LENGTH N

We prove a result related to the Erdos-Ginzburg-Ziv theorem: Let p and q be primes, alpha a positive integer, and m is-an-element-of {p(alpha), p(alpha)q}. Then for any sequence of integers c = {c1, c2, ..., c(n)} there are at least [GRAPHICS] subsequences of length m, whose terms add up to 0 modulo m (Theorem 8). We also show why it is unlikely that the result is true for any m not of the form p(alpha) or p(alpha)q (Theorem 9).