A Collage of Results on the Divisibility and Indivisibility of Class Numbers of Quadratic Fields

The investigation of the ideal class group \(Cl_K\) of an algebraic number field K is one of the key subjects of inquiry in algebraic number theory since it encodes a lot of arithmetic information about K. There is a considerable amount of research on many topics linked to quadratic field class groups notably an intriguing aspect is the divisibility of the class numbers. This article discusses a few recent results on the divisibility of class numbers and the Iizuka conjecture. We also discuss the quantitative aspect of the Iizuka conjecture.