Products of consecutive integers with unusual anatomy
Terence Tao
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 denotes the squarefree part of (the smallest factor of formed by dividing out a perfect square). For instance, we haveThe equation (1) ties into the general question of what the anatomy (prime factorization) of the product looks like. This is a venerable...