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One infinite family of solutions to the equation $a! = b! \times c!$ has $a = s!$ so we have $(s!)! = (s!-1)! \times s!$ but I'm hard pressed to find manually another type of solution apart from $10! = 7! \times 6!$. Is there a literature on this problem?


marked as duplicate by Wojowu, Saucy O'Path, Gerry Myerson elementary-number-theory Nov 30 '18 at 11:51

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  • $\begingroup$ Many thanks. I've now read the postings, noted the results - and the fact that to pursue the topic would be beyond me. $\endgroup$ – Paul Stephenson Dec 1 '18 at 13:57