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This question already has an answer here:

Is there any number which is a perfect square of some number as well as factorial of some number?

That is, let x be such a number, then x can be expressed as

             x = k^2 (for some k)

and, x = n! (for some n)

The very trivial answer is 1. But is there any number other than 1?

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marked as duplicate by José Carlos Santos, Parcly Taxel, Community Oct 6 '18 at 15:45

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ If this is true, there is no prime that is larger than $\frac{p}{2}$ and less than or equal to $p$, where $p$ is some solution. $\endgroup$ – Boshu Oct 6 '18 at 14:11
  • $\begingroup$ $$7!=71^2. {}{}{}{}{}{} $$ $\endgroup$ – MJD Oct 6 '18 at 17:39