Let's say that I have a finite field K with characteristic 2. I define @ as a map where
@ : K -> K, and
x -> $x^2$.
First of all, what are some examples of fields like K? I initially thought it would only be 0 and 1 with addition and multiplication mod 2, but apparently more elements can exist so long as 1+1=0.
Secondly, how would one begin to prove that @ is an automorphism?
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