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On the $p$-divisibility of class numbers of an infinite family of imaginary quadratic fields $\mathbb{Q} (\sqrt{d})$ and $\mathbb{Q} (\sqrt{d+1}).$ (2005.12084v2)
Published 25 May 2020 in math.NT
Abstract: For any odd prime $p,$ we construct an infinite family of pairs of imaginary quadratic fields $\mathbb{Q}(\sqrt{d}),\mathbb{Q}(\sqrt{d+1})$ whose class numbers are both divisible by $p.$ One of our theorems settles Iizuka's conjecture for the case $n=1$ and $p >2.$
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