Problem Statement
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?
Categories:
Number Theory
Progress
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.See also [363] and [931].
Source: erdosproblems.com/388 | Last verified: January 14, 2026