# Category:Definitions/Gaussian Primes

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This category contains definitions related to Gaussian Primes.

Related results can be found in **Category:Gaussian Primes**.

### Definition 1

Let $x \in \Z \sqbrk i$ be a Gaussian integer.

$x$ is a **Gaussian prime** if and only if:

- it cannot be expressed as the product of two Gaussian integers, neither of which is a unit of $\Z \sqbrk i$ (that is, $\pm 1$ or $\pm i$)
- it is not itself a unit of $\Z \sqbrk i$.

### Definition 2

A **Gaussian prime** is a Gaussian integer which has exactly $8$ divisors which are themselves Gaussian integers.

## Pages in category "Definitions/Gaussian Primes"

The following 3 pages are in this category, out of 3 total.