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Question Number 21598 by Tinkutara last updated on 29/Sep/17
Prove that ((n^2 !)/((n!)^n )) is an integer, n ∈ N.
$${Prove}\:{that}\:\frac{{n}^{\mathrm{2}} !}{\left({n}!\right)^{{n}} }\:{is}\:{an}\:{integer},\:{n}\:\in\:{N}. \\ $$

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