A comment on the equation $n!!=a_1!!\cdots a_t!!$

TL;DR

This paper explores the equation involving double factorials, demonstrating that under specific conditions, the abc conjecture implies only finitely many solutions exist.

Contribution

It establishes a connection between the abc conjecture and the finiteness of solutions to a factorial equation in special cases.

Findings

In certain cases, the abc conjecture implies finitely many solutions.

The study links factorial equations to deep conjectures in number theory.

Provides conditions under which solutions are finite.

Abstract

We study the equation $a_1!!\cdots a_t!!=n!!$ and show that in certain special cases the explicit abc conjecture implies that it has only finitely many nontrivial solutions.