Let $x=a+bi$ be an arbitrary Gaussian integer and consider the qoutient ring $S := \frac{\mathbb{Z}[i]}{(x)}$. I know that the number of elements of $S$ is equal to $a^2 + b^2$. Is it true that $S$ is isomorphic to $\mathbb{Z}_{a^2+b^2}$ (as rings)?
2026-03-25 06:05:15.1774418715
Homomorphic images of Gaussian Integers
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HINT: Consider Gaussian integers that are (normal) integers.