Theorem

Baker–Heegner–Stark theorem on $\mathbb Q[\sqrt{d}]$

If $d<0$ is an integer, then $\mathbb Q[\sqrt{d}]$ is a UFD iff $d \in \{\, -1, -2, -3, -7, -11, -19, -43, -67, -163\,\}$

Link: https://en.wikipedia.org/wiki/Stark%E2%80%93Heegner_theorem

Reference(s)

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