Question 29
Consider a polynomial $P(x) = (x+d_1)(x+d_2) \cdots (x+d_9)$, where $d_1, d_2, \ldots, d_9$ are nine distinct integers.
Prove that there exists an integer $N$ such that for all integers $x \ge N$ the number $P(x)$ is divisible by a prime number greater than 20.
Prove that there exists an integer $N$ such that for all integers $x \ge N$ the number $P(x)$ is divisible by a prime number greater than 20.