Problem 388

Erdős Problem #388: declared status 'open'. Formalized: no. 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? Current best: More generally, if $k_1>2$ then for fixed $a$ and $b$$$a\prod_{1\leq i\leq k_1}(m_1+i)=b\prod_{1\leq j\leq k_2}(m_2+j)$$should have only a finite number of solutions. Prize: no. Tags: number theory.