Monic polynomials with simple roots problem

annarodriguez

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Joined
Mar 18, 2019
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5
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
Joined
Mar 18, 2019
Messages
5
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...
 
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