Let a E Z, be a zero of the irreducible polynomial x + x +1 over Z,. Show that the Frobenius automorphism ơ2 of Z2(a) permutes the elements of A = {a,a², a + a²} and B = {1+a, 1+ a², 1+ a + a²}. %3D

Advanced Engineering Mathematics
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Let a E Z, be a zero of the irreducible polynomial x³ + x + 1 over Z2.
Show that the Frobenius automorphism ơ2 of Z2(@) permutes the elements of
A = {a, a², a + a²} and B = {1+a, 1+a²,1+a +a²}.
Transcribed Image Text:Let a E Z, be a zero of the irreducible polynomial x³ + x + 1 over Z2. Show that the Frobenius automorphism ơ2 of Z2(@) permutes the elements of A = {a, a², a + a²} and B = {1+a, 1+a²,1+a +a²}.
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