AbstractWe prove a result related to the Erdős‐Ginzburg‐Ziv theorem: Letpandqbe primes, α a positive integer, andm∈{pα,pαq}. Then for any sequence of integersc= {c1, c2,…, cn} there are at least(⌊12n⌋m)+(⌈12n⌉m)subsequences of lengthm, whose terms add up to 0 modulom(Theorem 8). We also show why it is unlikely that the result is true for anymnot of the formpαorpαq(Theorem 9).