All monic polynomials of degree $d$ such that $f(x) | f(x^n) \forall n \in \mathbb{Z}^+$? The coefficients may be complex.
I was doing a problem for $d=4$ and am wondering if this can this problem be generalized for any $d$

$x$ root of $f(x)$ $\Rightarrow$ $x^n$ root of $f$ $\forall n$, but $f$ has only a finite number of roots $\Rightarrow$ $x=0$ or a $k-$th root of unit $\Rightarrow$ $f(x)$ is...
