, r} be the orbit of under Gal(L/F), and let h = \prod_{i=1} r (x i).

Can anyone please help with this

Let F ⊂ L be a normal extension, let α ∈ L, let {α1, . . . , αr} be the orbit of α under Gal(L/F), and let h = r (x − αi). Show that there is an integer m such that

 (x − σ(α)) = h m (note that we are not assuming that F is the fixed field of Gal(L/F), so we are not claiming that h ∈ F[x]).