ISL 2012 N5

For a nonnegative integer $n$ define $\operatorname{rad}(n)=1$ if $n=0$ or $n=1$, and $\operatorname{rad}(n)=p_{1} p_{2} \cdots p_{k}$ where $p_{1}<p_{2}<\cdots<p_{k}$ are all prime factors of $n$. Find all polynomials $f(x)$ with nonnegative integer coefficients such that $\operatorname{rad}(f(n))$ divides $\operatorname{rad}\left(f\left(n^{r a d(n)}\right)\right)$ for every nonnegative integer $n$.