Notes on the divisibility of the class numbers of certain imaginary quadratic fields

TL;DR

This paper constructs infinite families of imaginary quadratic fields with class numbers divisible by any specified positive integer, advancing understanding of class number divisibility in number theory.

Contribution

It introduces new methods to generate infinite families of imaginary quadratic fields with prescribed divisibility properties of their class numbers.

Findings

Infinite families of imaginary quadratic fields with class number divisible by a given integer

New techniques for constructing such fields

Enhanced understanding of class number divisibility patterns

Abstract

In this paper, we construct certain infinite families of imaginary quadratic fields whose class number is divisible by a given positive integer.