For some non-zero Gaussian integer n, how can I find a finite upper bound for the number of congruence classes mod n?
2026-03-26 04:29:27.1774499367
Congruence Classes in the Guassian Integers?
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If $n = a + bi$, then there will be $a^2 + b^2$ distinct residue classes. Proving this in the $\mathbb{Z}[i]$ case may be done with the Euclidean algorithm (and some work.) However, it is a general fact of number fields that the number of distinct residue classes is given by a norm function.