Problems in Galois Theory

a Let K be a field of characteristic p > 0, and let c inK Show that if alpha is a root of f (x) = x^p – x – c, so is alpha + 1 Provethat K(alpha) is Galois over K with group either trivial or cyclic of order p

b Find all subfields of Q ( sqrt2, sqrt 3) with proof thatyou have them all What is the minimal polynomial of sqrt2+ sqrt3? Whichsubfields does it generate over Q?

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