(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have the field [tex] F_5 [/tex] and I adjoin some square root of 2 , say [tex]2^{1/4}[/tex]. Is there a way to see that the multiplicative group inside [tex]F_5(2^{1/4})[/tex] is cyclic and find the generator?

2. Relevant equations

3. The attempt at a solution

I did the [tex]F_5(2^{1/2})[/tex] case and think the generator is [tex]2+\sqrt{2}[/tex]. But don't know how this generalizes..

Thanks!

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# Homework Help: Adjoining element to a field

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