Irreducible polynomial, cyclic group

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Describe the field F=\frac{\mathbb{F}_3[x]}{(p(x))} [p(x) is an irreducible polynomial in \mathbb{F}_3[x]]. Find an element of F that generates the cyclic group F^* and show that your element works.

[p(x)=x^2+1 is irreducible in \mathbb{F}_3[x] if that helps]
 
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I've already given you a warning about posting your homework questions without showing your attempts to work on the problem. Continuing to do so will not be tolerated.
 
Not to mention this should be in the Abstract Algebra forum.

Write the elements of F explicitly (in terms of, say, t, where t2 + 1 = 0). Find one that has order 8.
 

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