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Infinite families of pairs of real quadratic fields whose class numbers are divisible by a given integer
Abstract
For any integers N ≥ 2 and m ≥ 1, we prove that there exist infinitely many pairs of real quadratic fields QQ(√D), QQ(√(D + m)), with D ∈ ZZ and D > 0, such that the class numbers of both fields are divisible by N. Write N = 2en 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
@misc{iizuka2026infinite,
title = {{Infinite families of pairs of real quadratic fields whose class numbers are divisible by a given integer}},
author = {Yoshichika Iizuka},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27434},
eprint = {2609.27434},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27434},
}
RIS
TY - UNPB
TI - Infinite families of pairs of real quadratic fields whose class numbers are divisible by a given integer
AU - Yoshichika Iizuka
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27434
UR - https://arxiv.org/abs/2609.27434
AB - For any integers N ≥ 2 and m ≥ 1, we prove that there exist infinitely many pairs of real quadratic fields QQ(√D), QQ(√(D + m)), with D ∈ ZZ and D > 0, such that the class numbers of both fields are divisible by N. Write N = 2^en with n odd. If n > 1, then the class groups of both fields in each such pair contain an element of order n.
ER -