Problem is:
Produce elements a and b in the domain $R := \{x+2y\sqrt{-1} \mid x, y \in \mathbb{Z}\}$ having no gcd.
How can produce this? Actually I use norm function, and brute force, but what I found is that, except in case of y = 4, so many values of norm function are prime. So I can't handle it. Do you have any idea?