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

Jaitra Chattopadhyay, Subramani Muthukrishnan

Let $k\ge 1$ be a cube-free integer with $k\equiv 1(\mathrm{mod}9)$ and $\gcd (k,7\cdot 571)=1$. In this paper, we prove the existence of infinitely many triples of imaginary quadrat…