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Erdős problem 397

Are there only finitely many solutions to ∏i(2mimi)=∏j(2njnj) \prod_i \binom{2m_i}{m_i}=\prod_j \binom{2n_j}{n_j} with the mi,njm_i,n_j distinct?
Retained from Formal Conjectures · not edited here
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Accepted in Vela Mathematics Program

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