Let $\zeta_n$ be the $n$th root of unity. The wikipedia page for unique factorization domain (UFD) states that for $n \in \mathbb Z$, $1 \le n \le 22$, $\mathbb Z[\zeta_n]$ is a UFD, but not for $n = 23$. Is there a general formula for determining when an integer extension with a root of unity is a UFD? Failing that, is it known for higher $n$ than $23$?
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2this may be of interest. – Sep 18 '17 at 15:44
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Ah, so only $n$ with class number 1 is a UFD, correct? Thanks for the link! I haven't yet been able to find how a class number is calculated. Really interesting history about Kummer's work and Fermat's Last Theorem. – hatch22 Sep 18 '17 at 15:58
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See also this question, or this one. – Dietrich Burde Sep 18 '17 at 16:08
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Note that it is UFD if and only it is PID. – Dietrich Burde Sep 18 '17 at 16:15
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Oops! Sorry for asking a duplicate. That question didn't come up when I searched, but it is clearly the same. Should I delete my question? – hatch22 Sep 18 '17 at 16:21
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Don't worry, just leave it. It might be of help to somebody else who's searching for the same thing. – Hans Lundmark Sep 18 '17 at 18:57