IMO 1967 - Official Contest Problems Question 3

Let $k,m,n$ be positive integers such that $m+k+1$ is a prime number greater than $n+1$. Write $c_s$ for $s(s+1)$. Prove that the product $(c_{m+1}-c_k)(c_{m+2}-c_k)\cdots(c_{m+n}-c_k)$ is divisible by the product $c_1c_2\cdots c_n$.