I'm pretty sure that I should apply the pigeon hole principle, but I'm not sure exactly how.

Let a_i with i ranging from 1 through n be a sequence of integers (both positive and negative, not necessarily all different). Prove that there exists integers j and k with 1 <= j <= k <= n such that the sum starting from a_j and ending at a_k (ie, the sum of some subsequence of the sequence) sums to a multiple of n