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On divisibility of the class number of real octic fields of a prime conductor $$p=n^ 4+16$$ by $$p$$. (English) Zbl 0818.11042
Let $$K$$ be a real octic subfield of the $$p$$-th cyclotomic field, where $$p$$ is a prime of the form $$n^ 4+16$$. The author proves that $$p$$ divides the class number of $$K$$ if and only if $$p$$ divides the numerator of at least one of the Bernoulli numbers $$B_{j(p- 1)/8}$$ for $$j=1,3,5,7$$. In a previous work [Abh. Math. Semin. Univ. Hamb. 64, 105- 124 (1994)] he used a similar method to obtain an analogous result for quintic fields.
##### MSC:
 11R29 Class numbers, class groups, discriminants 11R18 Cyclotomic extensions 11B68 Bernoulli and Euler numbers and polynomials 11R20 Other abelian and metabelian extensions
##### Keywords:
cyclotomic field; Bernoulli numbers
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