# Math Help - how to prove

1. ## how to prove

How to prove that the fields F2[x]/ (x^4+x+1) and F2[x]/ (x^4+x^3+x^2+x+1) are isomorphic. can any one explain it to me .

2. Hint :

Denote:

$I=(x^4+x+1)$

then,

$\mathbb{F}_2[x]/ I=\left\{{a_3x^3+a_2x^2+a_1x+a_0+I:a_i\in \mathbb{F}_2}\right\}$

Idem for $J=(x^4+x^3+x^2+x+1)$ .

Fernando Revilla