The aim of this paper is to prove the following Theorem Theorem Let $K$ be an octic subfield of the field $Q(\zeta _p+\zeta _p^{-1})$ and let $p=n^4+16$ be prime. Then $p$ divides $h_K$ if and only if $p$ divides $B_j$ for some $j=\frac{p-1}{8}$, $3\frac{p-1}{8}$, $5\frac{p-1}{8}$, $7\frac{p-1}{8}$.
@article{107512,
author = {Stanislav Jakubec},
title = {On divisibility of the class number of real octic fields of a prime conductor $p=n\sp 4+16$ by $p$},
journal = {Archivum Mathematicum},
volume = {030},
year = {1994},
pages = {263-270},
zbl = {0818.11042},
mrnumber = {1322570},
language = {en},
url = {http://dml.mathdoc.fr/item/107512}
}
Jakubec, Stanislav. On divisibility of the class number of real octic fields of a prime conductor $p=n\sp 4+16$ by $p$. Archivum Mathematicum, Tome 030 (1994) pp. 263-270. http://gdmltest.u-ga.fr/item/107512/
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