Consider a polynomial
![P(x) = \prod^9_{j=1}(x+d_j),](/media/m/c/7/3/c73825eafaf6ac452f140cd1ecbbd779.png)
where
![d_1, d_2, \ldots d_9](/media/m/1/a/c/1ac2cb9f7446ec02617aea33463c2528.png)
are nine distinct integers. Prove that there exists an integer
![N,](/media/m/7/9/a/79a4f22a4522fc99b6f195180241b267.png)
such that for all integers
![x \geq N](/media/m/3/5/e/35eb19507e3ebdd1618a7a9026622c8e.png)
the number
![P(x)](/media/m/c/d/7/cd7664875343d44cd5f96a566b582b0e.png)
is divisible by a prime number greater than 20.
Proposed by Luxembourg
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Consider a polynomial $P(x) = \prod^9_{j=1}(x+d_j),$ where $d_1, d_2, \ldots d_9$ are nine distinct integers. Prove that there exists an integer $N,$ such that for all integers $x \geq N$ the number $P(x)$ is divisible by a prime number greater than 20.
Proposed by Luxembourg