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5
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Classification of cyclotomic fields with class number 1
The complete list of $n$ for which ${\bf Q}(\zeta_n)$ has unique factorization is
1 through 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 40, 42, 44, 45, 48, 50, 54, 60, 66, 70, 84, 90.
Source; …