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Abstract: In this paper, Hajdua, Pappa, and Szakács prove that writing $k=B-A$ for all non-trivial solutions of the equation $A!B!=C!$ different from $(A, B, C) =(6, 7, 10)$, we have $C<5k$. Further, if $k<10^6$, then the only non-trivial solution is given by $(A, B, C) =(6, 7, 10)$.