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Let $\mathbb Z[i]$ denote the ring of Gaussian integers. For which of the following values of $n$ is the quotient ring $\mathbb Z[i]/n \mathbb Z[i]$ an integral domain?
$2,13,19,7$

How can I solve the problem?

  • 2
    Why do you post two questions within 5 minutes with two different user names?2012-12-05
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    when n is a gaussian prime, so 19 and 17 (because they equal 3 mod 4).2012-12-05

3 Answers 3