# Is there any number which is a perfect square of some number as well as factorial of some number. [duplicate]

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?

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

• 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. – Boshu Oct 6 '18 at 14:11
• $$7!=71^2. {}{}{}{}{}{}$$ – MJD Oct 6 '18 at 17:39