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 $23$?
2026-03-30 02:06:48.1774836408
When are the integers extended with the nth root of unity a unique factorization domain?
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