Erdős Problem #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?

#388: [Er76d][ErGr80][Er92e]

number theory

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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].

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5 comments on this problem

Likes this problem	old-bielefelder, Nik007
Interested in collaborating	Nik007
Currently working on this problem	Nik007
This problem looks difficult	None
This problem looks tractable	Nik007

Additional thanks to: Sarosh Adenwalla

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