Erdős-Ginzburg-Ziv theorem

If $a_1,a_2,\mathrm{\dots },a_{2n-1}$ is a set of integers, then there exists a subset $a_{i_1},a_{i_2},\mathrm{\dots },a_{i_n}$ of $n$ integers such that

$$a_{i_1}+a_{i_2}+\mathrm{\cdots }+a_{i_n}\equiv 0(modn).$$

The theorem is also known as the EGZ theorem.