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 August 6th, 2019, 01:10 PM #1 Senior Member   Joined: Dec 2015 From: somewhere Posts: 592 Thanks: 87 Prove division Prove that $\displaystyle 40m \: | \: (5m)! \;$ , $\displaystyle m\in \mathbb{N}.$
 August 6th, 2019, 01:46 PM #2 Global Moderator   Joined: May 2007 Posts: 6,806 Thanks: 716 Among the factors in 5m! are 5m, 4m, and 2m, which multiplied together is 40m$^3$, which is divisible by 40m. Thanks from topsquark
 August 6th, 2019, 01:50 PM #3 Senior Member     Joined: Sep 2015 From: USA Posts: 2,529 Thanks: 1389 $(5m)! = 5m \cdot \dfrac{(5m-1)!}{8!} \cdot 8 \cdot 7! = 40m \cdot \dfrac{(5m-1)!}{8}$ Thanks from topsquark

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