## Recreational question about factorials

Walking out of my Finite Math class I wondered if one can determine all possible triples of non-negative integers $(a,b,c)$ such that

$\displaystyle a!\ b!=c!$

There are some trivial solutions. Whenever $c=p!$ for some other non-negative integer $p$, then $(c-1,p,c)$ is a solution.

Are there any other? (I haven’t put much thought to this question).