For which integer $d$ is the ring $\mathbb{Z}[\sqrt{d}]$ norm-Euclidean?
Here I'm referring to $\mathbb{Z}[\sqrt{d}] = \{a + b\sqrt{d} : a,b \in \mathbb{Z}\}$, not the ring of integers of $\mathbb{Q}[\sqrt{d}]$.
For $d < 0$, it is easy to show that only $d = -1, -2$ suffice; but what about $d>0$?
Thanks.