I would like to show that $\mathbb{Z}[\phi]$ is a UFD, where $\phi^2+\phi+1=0$. I started with a division with remainder to determine the irreducibles, but I could not finish that, and I do not know how to approach this problem. Could you provide me with some resources or show how I can solve this? Thanks in advance.
2026-02-22 19:31:12.1771788672
Showing that $\mathbb{Z}[\phi]$ is a UFD, where $\phi^2+\phi+1=0$.
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