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Real quadratic fields with class numbers divisible by \(n\). (English) Zbl 0287.12007
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)].

MSC:
11R11 Quadratic extensions
11R29 Class numbers, class groups, discriminants
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References:
[1] Nagell, T, (), 140-150
[2] Mordell, L.J, ()
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