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frobenius map on primitive nth root of unity on Fp with (n,p)=1

Suppose w is a primitive n-th root of unity, let r = Ord_n(p), f(w)=w^p(the frobenius map), how to prove that w,f(w),f^2(w),...f^(r-1)(w) are all different in Fp(w) so that the minimal monic polynomial of w over Fp factors into those r factors in Fp(w)?