Irreducible polynomial, cyclic group

[mathsss2]

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]

 

[Hurkyl]

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.

 

[adriank]

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.