# Monic polynomials with simple roots problem

#### annarodriguez

##### New member
How can we find all the monic polynomials P(X) ∈ C [X], with simple roots such that P(Xn) = ±P(X) P(ζX) P (ζ2X) …P (ζn-1X), where ζ is a primitive n-th root of unity?

#### annarodriguez

##### New member
How can we find all the monic polynomials P(X) ∈ C [X], with simple roots such that P(Xn) = ±P(X) P(ζX) P (ζ2X) …P (ζn-1X), where ζ is a primitive n-th root of unity?
I was thinking that the roots of P(X) are included into the set of roots of the equation xn=x, but I'm honestly stuck on how I could prove this...