Hello,

the ring of gaussian integers $\displaystyle \mathbb Z[i]$ is isomorphic to the ring $\displaystyle \mathbb Z[x]/(x^2+1)$.

Using this fact, why are the rings $\displaystyle \mathbb Z[i]/p \mathbb Z[i]$ and $\displaystyle \mathbb F_p[x]/(x^2+1)\mathbb F_p[x]$ isomorphic?

Thanks in advance,

Alexander