Erdős Problem 388

### What is the conjecture

https://www.erdosproblems.com/388

Can one classify all solutions of
$$\prod_{1\leq i\leq k_1}(m_1+i)=\prod_{1\leq j\leq k_2}(m_2+j)$$
where $k_1,k_2>3$ and $m_1+k_1\leq m_2$? Are there only finitely many solutions?

Status: open

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else