Divisibility of the class numbers of imaginary quadratic fields

Abstract

For a given odd integer $n>1$, we provide some families of imaginary quadratic number fields of the form $\mathbb{Q}(\sqrt{x^2-t^n})$ whose ideal class group has a subgroup isomorphic to $\mathbb{Z}/n\mathbb{Z}$.

10 pages, accepted for publication in Journal of Number Theory (2017)