prove that if $f(x) \in \mathbb{Z}[x]$ and $f$ is non-constant, that for infinitely many $n, f(n)$ is not prime prove that if $f(x) \in \mathbb{Z}[x]$, that for infinitely many $n, f(n)$ is not prime.
I tried looking at the polynomial of that form $f(x) = \sum_{i\in \mathbb{N}}  a_ix^i$. I am kinda stuck her though, is it helpfull to look at the roots?
Kes

$f(kf(a)+a)-f(a)$ is a multiple of $f(a)$, so $f(x)$ is a multiple of $f(a)$ infinitely often.
