Summary: Let \(n>1\) be a positive integer and \(p\) be the smallest prime divisor of \(n\). Let \(S\) be a sequence of elements from \({\mathbb Z}_n={\mathbb Z}/n{\mathbb Z}\) of length \(n+k\) where \(k\geq {n\over p}-1\). If every element of \({\mathbb Z}_n\) appears in \(S\) at most \(k\) times, we prove that there must be a subsequence of \(S\) of length \(n\) whose sum is zero when \(n\) has only two distinct prime divisors.