Abstract
For a given odd positive number n and a positive integer m, we show that there exist infinitely many pairs of imaginary quadratic fields \( {\mathbb {Q}}(\sqrt{D}) \) and \( {\mathbb {Q}}(\sqrt{D+m}) \) with \(D\in {\mathbb {Z}}\) whose class groups have an element of order n.
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We would like to thank the anonymous referee for the valuable comments and suggestions.
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Xie, JF., Chao, K.F. On the divisibility of class numbers of imaginary quadratic fields (\( {\mathbb {Q}}(\sqrt{D}), {\mathbb {Q}}(\sqrt{D+m})\)). Ramanujan J 53, 517–528 (2020). https://doi.org/10.1007/s11139-019-00217-1
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DOI: https://doi.org/10.1007/s11139-019-00217-1