Hello!
Is there something wrong in the problem 6.3?
Why does it say $x^4+3x+1+5$? Also its like impossible to find a finite field where this polynomial is irreducible in
Yes it should just be +1
Oh ok that makes it much more doable then, because we cant draw the conclusion that the Galois group has a 4 cycle just because the polynomial is irreducible over Q, right?
Thanks (:
Thanks (:
On a related note; is problem 6.2 what you intended? I never used that we are in F_3 in my q(X) such that (X^4-1)q(X) = X^9-X.
(I realize that perhaps you intend one to use these results later in the problem; I am not sure how right now, but if that is the case then this might explain why, although I recall I did have to use that we were in F_2 on 6.1 so...).
(I realize that perhaps you intend one to use these results later in the problem; I am not sure how right now, but if that is the case then this might explain why, although I recall I did have to use that we were in F_2 on 6.1 so...).