Iizuka's successive quadratic fields conjecture

Let $p$ be a prime number and let $m$ be a positive integer. For an integer $d$, consider the $m+1$ successive quadratic fields

$$\mathbb{Q}(\sqrt{d}),\mathbb{Q}(\sqrt{d+1}),\cdots,\mathbb{Q}(\sqrt{d+m}).$$

Here, “real (or imaginary) quadratic” means that the corresponding squarefree radicands give real (or imaginary) quadratic fields, and the class number is the cardinality of the ideal class group. Iizuka's conjecture. For any prime number $p$ and any positive integer $m$, there is an infinite family of $m+1$ successive real (or imaginary) quadratic fields of this form, with $d\in\mathbb{Z}$, whose class numbers are all divisible by $p$. Iizuka formulated this as a generalization of the existence results for pairs of successive imaginary quadratic fields; the conjecture asks for arbitrarily long successive tuples and is not stated as resolved in the source.