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I have bumped into one simple task which I am not able to prove:

How to prove, that number $ \frac{1000!}{(100!)^{10}} $ is integer?


marked as duplicate by Dietrich Burde number-theory Feb 19 at 19:06

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  • $\begingroup$ $(100\cdot 10)!$ is divisible by $100!^{10}$ by the duplicate. $\endgroup$ – Dietrich Burde Feb 19 at 19:09
  • $\begingroup$ ok sorry as I see there is already same questions, ty lads anyway sry for stupidness $\endgroup$ – Tovarisch Feb 19 at 19:10

The given number is a multinomial coefficient, which is always an integer.


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