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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
##### Keywords:
real quadratic fields; divisibility of class number
Full Text:
##### References:
 [1] Nagell, T, (), 140-150 [2] Mordell, L.J, ()
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