Subset of $\mathbb{Z}_n$ and zero sum

Question

Let $a_1, a_2, \ldots, a_n$ be elements of $\mathbb{Z}_n$. Prove that there exist $r$ and $s$ such that $\sum_{i=r}^s a_i \equiv 0 \pmod n$ (with $1 \leq r \leq s \leq n$).

Do you have any hint? I have no ideas

Answer 1

Hint: Use the pigeonhole principle on the partial sums $\sum_{i=1}^s a_i$ for $1\leq s\leq n$.