Infinite families of pairs of real quadratic fields whose class numbers are divisible by a given integer

Yoshichika Iizuka

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arXiv · 2609.27434

Infinite families of pairs of real quadratic fields whose class numbers are divisible by a given integer

Yoshichika Iizuka

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Abstract

For any integers $N \ge 2$ and $m \ge 1$, we prove that there exist infinitely many pairs of real quadratic fields $\QQ(\sqrt{D}), \QQ(\sqrt{D + m})$, with $D \in \ZZ$ and $D > 0$, such that the class numbers of both fields are divisible by $N$. Write $N = 2^{e}n$ with $n$ odd. If $n > 1$, then the class groups of both fields in each such pair contain an element of order $n$.

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BibTeX RIS

Yoshichika Iizuka. 2026-09-23. Infinite families of pairs of real quadratic fields whose class numbers are divisible by a given integer. https://arxiv.org/abs/2609.27434

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