Question 80
For nine distinct positive integers $d_1,d_2,\ldots,d_9$, consider $P(n)=(n+d_1)(n+d_2)\cdots(n+d_9)$. Prove that there exists an integer $N$ such that for every integer $n\geq N$, the number $P(n)$ is divisible by a prime greater than $20$.