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**hunkydory19** $\displaystyle g = X^4 + X + 1 $ over F2 and let E be the extension of F2 with a root alpha of g.

Show that every non-zero element of E is a power of $\displaystyle \alpha$.

I can do this question which is worth 8 marks...but cannot do:

Show that if $\displaystyle \beta$ is an element of E - F2 then every non-zero element of E is a power of $\displaystyle \beta$.

Which is worth 4 marks...I'm guessing this answer is much easier since it is only 4 marks, so there is a way I can adapt my answer to the former question for this one? Or is it a totally different method?

Thanks in advance!