Odd gaussian primes

Question

What we mean when we say odd gaussian prime and is there even gaussian primes?

Also is there odd and even gaussian integers?

I haven't heard that before, and you haven't told us the context where this appears (which would greatly help our ability to guess what it could mean), but an idea is that it means "odd prime that is also a Gaussian prime". Would that make sense? — Arthur, Aug 14 '20 at 10:56

score 3 · Accepted Answer · answered Aug 14 '20 at 11:02

A Gaussian integer is called even if its norm is an even integer.

Proposition: A Gaussian integer has even norm if and only if it is a multiple of $1 + i$.

Reference: Notes by Keith Conrad on Gaussian integers.

The wikipedia page on Gaussian integers also defines even and odd Gaussian integers.

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