Curious about this post on, $$6!7!=10!\tag1$$ a little Mathematica expt yielded, $$r!(r!-1)!=(r!)!\tag2$$
Q: Are the only non-trivial integer solutions to $\color{blue}{a!b!=c!}$ with $a,b>1$ given by $(1)$ and $(2)$?
2026-04-07 12:56:01.1775566561
Are these the only solutions to $a!b!=c!$?
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