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Can we explicitly solve $n$ in terms of $a$? Can we rewrite this inequality in the form of $n>f(a)$ without using $n!$ the factorial?

Sekots Reivan
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    Well I guess you could extend factorial to gamma function and restrict the domain to a strictly increasing region so that the gamma function is invertible. Then you have $n>\Gamma^{-1}(a)$ – ASKASK Apr 18 '16 at 01:31

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