Weinberger, P. J. Real quadratic fields with class numbers divisible by \(n\). (English) Zbl 0287.12007 J. Number Theory 5, 237-241 (1973). From the introduction: The goal of this note is to prove the following theorem: Theorem 1: For all positive integers \(n\), there are infinitely many real quadratic fields \(\mathbb Q(\sqrt{\Delta(x)})\) with class numbers divisible by \(n\), where \(\Delta(x) = x^{2n} + 4\).The corresponding theorem for complex quadratic fields was originally proved by T. Nagell [Abh. Math. Sem. Univ. Hamb. 1, 140–150 (1922; JFM 48.0170.03)]. Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 32 Documents MSC: 11R11 Quadratic extensions 11R29 Class numbers, class groups, discriminants Keywords:real quadratic fields; divisibility of class number PDF BibTeX XML Cite \textit{P. J. Weinberger}, J. Number Theory 5, 237--241 (1973; Zbl 0287.12007) Full Text: DOI References: [1] Nagell, T, (), 140-150 [2] Mordell, L.J, () This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.