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For an odd prime number p and an integer n ≥ 0, let hn be the class number of the pn+1st cyclotomic field Q($$ \zeta _{p^{n + 1} }  $$). It is known that when p = 3 or 5, hn is odd for all n ≥ 0. We prove that the same holds also when p = 7.

On the parity of the class number of the 7nth cyclotomic field