Prove Gaussian Integer is prime?

Asked Feb 29 '16 at 23:43

Active Feb 29 '16 at 23:43

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How can I prove that a Gaussian integer is prime? For instance, how can I prove that $7+0i$ is a prime number?

On wikipedia, I found that a Gaussian integer is prime either if its norm is a prime in the real numbers, or if either the real or imaginary part of the number is zero, while the other part is of the form 4+3n, but this doesn't seem like a sufficient proof.

asked Feb 29 '16 at 23:43

Philip J Fry

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A start is to prove there's no Gaussian integer with norm 7. – Gerry Myerson Feb 29 '16 at 23:45
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Just a curiosity: is it a homework question from your number theory class? – Anurag A Feb 29 '16 at 23:48
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Also Prime elements in the gaussian integers – Feb 29 '16 at 23:49
Not entirely a duplicate of the other threads, as both of them are about $4k+3$ primes only. Fry's question also is about the fact that for non-real $z$, $z$ is prime if and only if $z^*z$ is prime. – Paul Sinclair Mar 01 '16 at 04:39

Prove Gaussian Integer is prime?

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