Recent content by aadams

Thank you very much for your help! I'm still a bit confused on part (b) - I can see that α^4=α+1 and how this helps to write elements as α^n. I'm not sure how I could write elements such as α^2 + 1 and α^2+α+1 as α^n?? Also with other elements α^3+α, α^3+1, α^3+α^2+α, α^3+α+1 and α^3+α^2+α+1...

I am really struggling on the following Algebra question: Consider the Irreducible Polynomial g = X^4 + X + 1 over 𝔽2 and let E be the extension of 𝔽2 = {0,1} with root α of g. (a) How many elements does E have? (b) Is every non-zero element of E of the form α^n with n ϵ N (natural numbers)...