2002 IMO Shortlist Problems/N5

Problem

Let $m, n$ are integers greater than $1$ . $a_1, a_2, ... , a_n$ are integers, and none is a multiple of $mn-1$ . Show that there are integers $e_i$ , not all zero, with $|e_i| < m$ , such that $e_1a_1 + e_2a_2 + ... + e_na_n$ is a multiple of $mn$ .

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2002 IMO Shortlist Problems/N5

Problem