NOTE ON THE p-DIVISIBILITY OF CLASS NUMBERS OF AN INFINITE FAMILY OF IMAGINARY QUADRATIC FIELDS

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=1and $p...