Let $f(x)$ denote a polynomial of degree at least $1$ with integer coefficients and positive leading coefficient.
(i) Show that if $f(x_0) =m >0$, then $$f(x)\equiv0 \mod m$$ whenever $$x\equiv x_0 \mod m.$$ (ii) Show that there are infinitely many $x\in \mathbb{N}$ such that $f(x)$ is not prime.
I have finished the first question but can someone help me with the second part? Thanks a lot!