International Mathematical Olympiad 1977 Problem 3

Let $n$ be a given integer $> 2$, and let $V_n$ be the set of integers $1 + kn$, where $k = 1, 2, \ldots$. A number $m \in V_n$ is called indecomposable in $V_n$ if there do not exist numbers $p, q \in V_n$ such that $pq = m$. Prove that there exists a number $r \in V_n$ that can be expressed as the product of elements indecomposable in $V_n$ in more than one way. (Products which differ only in the order of their factors will be considered the same.)