# Prove that there exist at most 2 non-isomorphic fields of order 4.

#### Solution Preview

Proof:

We know that F=Z2={0,1} is a field with order 2, f(x)=x^2+x+1 is an irreducible polynomial

in F. Then F[x]/(f(x))=F[x]/(x^2+x+1)={0,1,x,x+1} is a field with order 4.

Because there is ...

#### Solution Summary

It is proven that there exist at most 2 non-isomorphic fields of order 4.

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