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25 Dec 2021Mathchan is launched into public

2 / 1 / 2 / ?

File: 20220730_133901.jpg ( 37.3 KB , 1024x664 , 1659270843623.jpg )

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Is there a solution for this equation:
x = x!^n
I'm dumb af
>>
>>10
Yes. You are asking whether $\log x= n\log\Gamma(x+1)$ for some $x$, and presumably some $n$ which is given. It is easy to see that at least for some $n$, such as $n=1,$ this must have (at least) one solution, if you think about the shape of the graphs.
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>>11
Oh also, there is of course the trivial solution
x=1x=1
but there is another since the curves have to intersect again.