Recreational question about factorials

Walking out of my Finite Math class I wondered if one can determine all possible triples of non-negative integers (a,b,c) such that

\displaystyle a!\ b!=c!

There are some trivial solutions. Whenever c=p! for some other non-negative integer p, then (c-1,p,c) is a solution.

Are there any other? (I haven’t put much thought to this question).

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