As the question title suggests, is it true that $\mathbb{Z}[i]/m\mathbb{Z}[i]$ has exactly $\text{N}(m)$ elements?
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3What is N($m$)? – Jul 26 '16 at 16:29
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1Yes, the cardinality of the quotient is the norm of $m$. If $K$ is a number field and $A$ is its ring of integers, then for any non-zero element $a$ of $A$, the quotient $A/(a)$ has cardinality $N_{K/\Bbb Q}(a)$. – Watson Jul 26 '16 at 16:30
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By the way, are you the same user who asked this question? If yes, you should merge them. – Watson Jul 26 '16 at 16:33