A Gaussian prime?

Number Theory Level 2

$\large z = 13 + 13i$

You can't tell Yes No

2 solutions

Geoff Pilling
Jan 20, 2017

In order for $z = a + bi$ to be a Gaussian prime, then $a^2 + b^2$ must be a prime number.

$13^2 + 13^2 = 338$

And $338$ is not prime.

So, $\boxed{\text{no}}, \; z$ is not a Gaussian prime.

I am not sure how this solution works. For example 3 is a Gaussian prime but the norm is 9 which is not prime.

math monkey - 2 weeks, 4 days ago

Jose Fernandez Goycoolea
Nov 18, 2017

$13+13i=(1+i)(3+2i)(3-2i)$ is the prime decomposition.