## Compute the greatest common divisor of two ideals in ZZ[sqrt(-5)]

Compute the greatest common divisor of the ideals $(1-2\sqrt{-5})$ and $(2)$ in $\mathbb{Z}[\sqrt{-5}]$.

Recall that $((1-2\sqrt{-5}),(2)) = (1-2\sqrt{-5},2)$. Since $1 = 1-2\sqrt{-5} + 2\cdot \sqrt{-5}$, this ideal contains 1, and so $((1-2\sqrt{-5}),(2)) = (1)$.