This is a problem I encountered on a competition Discord server, apparently, there is an elementary solution, but I'd honestly be fine with any solution.
Wolfram Alpha solves the problem, here's the link (so that people who don't want to see it don't have to).
The problem is to solve (within positive integers) the following: $$a(a+1)=b!(b+2)$$
I've tried using Bertrand's postulate, bounding, and coming up with some counting arguments, all methods have failed.