Find the Addition and Multiplication tables for GF(7).
I know in order to do this, I have to express it in terms of $Z_7[x]/(x+1)$, or some other irreducible polynomial of order 1. But I'm not sure how to proceed from here. Any help would be great, thank you in advance!
Well, $GF(7) = {\Bbb Z}_7$. No need to consider polynomials. Just work modulo $7$.