We know that UFDs are integrally closed. But there is no theorem which states that Integrally Closed are UFD. So I wonder there should be a counter-example. I know that $Z[\sqrt{4k+2}$ and $\mathbb{Z}[\sqrt{4k+3}$ are integrally closed. I wonder which of them is not a UFD.
If no such example from $\mathfrak{O}_k$ , exists then can anyone give me an easier to understand example?
