In this note, the authors extend the main result from [\textit{F. Luca}, Rocky Mt. J. Math. 29, No. 4, 1387--1411 (1999; Zbl 0978.11010)] and prove the following Theorem: The largest solution of the Diophantine equation \[ F_{n_1}\dots F_{n_k}=m_1!\dots m_t!, \] where \(0<n_1<\dots<n_k\) and \(1\leq m_1\leq m_2\leq\dots\leq m_t\) are integers, is \[ F_1F_2F_3F_4F_5F_6F_8F_{10}F_{12}=11!. \]
Diophantine equations involving faculties
scientific article; zbMATH DE number 5079773