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10!/7!=6!. 6!/3!=5!. Is there something interesting happening in these examples, or are they just coincidence? Is there a way of finding other examples like these?

Brayden
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    I think this has been already asked and I also think that those are coincidences. Of course there are trivial solution as $$\frac{24!}{23!}=4!$$ but I think you do not want to consider them. – Peter Jan 13 '22 at 17:57
  • By the way, the second equation actually is such a "trivial" solution , just rearranged. – Peter Jan 13 '22 at 18:01
  • @lulu Is $(6,7,10)$ the only "nontrivial" solution with three numbers ? – Peter Jan 13 '22 at 18:05
  • @Peter It was, as of a few years ago anyway. The links attached to the duplicate should have reasonably current information. Anyway, I believe it's the only example. – lulu Jan 13 '22 at 18:09

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