Complex polynomials with simple roots problem

Mar 2019
3
0
Romania
What are all the monic polynomials P(X) ∈ C [X], with simple roots such that P(X^n) = ±P(X) P(ζ*X) P (ζ^2*X) …P (ζ^(n-1)*X), where ζ is a primitive n-th root of unity?