Products of consecutive integers with unusual anatomy

I’ve just uploaded to the arXiv my paper “Products of consecutive integers with unusual anatomy“. This paper answers some questions of Erdős and Graham which were initially motivated by the study of the Diophantine factorial equation where and are positive integers. Writing , one can rewrite this equation as where denotes the squarefree part of (the smallest factor of formed by dividing out a perfect square). For instance, we have which corresponds to the solution to the original equation. The e...