# The diophantine equation $a! = b! \times c!$ [duplicate]

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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 StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Nov 30 '18 at 11:51

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