On the simultaneous 3-divisibility of class numbers of triples of imaginary quadratic fields

Let k \geq 1be a cube-free integer with k \equiv 1 \pmod {9}and \gcd (k, 7\cdot 571)= 1 We prove the existence of infinitely many triples of imaginary quadratic fields \mathbb {Q}(\sqrt {d}) \mathbb {Q}(\sqrt {d+1})and $\mathbb {Q}(\sqrt...