Find all solutions in positive integers a; b; c to the equation(adsbygoogle = window.adsbygoogle || []).push({});

a!b! = a! + b! + c!

I have rearranged and got (a!-1)(b!-1) = c!+1

And the only solutions I can find are a=3 b=3 c=4 but I can't be sure that they are the only ones. How would I go about finding other solutions?

I have tried b=1 to 4 but after that the numbers start getting a bit big

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# Homework Help: Find all solutions in positive integers

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