Exercise
Consider the field F = Z/2Z[X]/(X3 + X + 1). Which element of F listed below is not the image of x = X + (f) under an automorphism of F?
x + 1
x2
x2 + x
Correct. f(x + 1) = x2 + x 
0.
0.
No. Since x is a root, so is x2.
No. Since x is a root, so is x4 =
x2 + x.