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.

August 6th, 2019, 01:50 PM  #3 
Senior Member Joined: Sep 2015 From: USA Posts: 2,529 Thanks: 1389 
$(5m)! = 5m \cdot \dfrac{(5m1)!}{8!} \cdot 8 \cdot 7! = 40m \cdot \dfrac{(5m1)!}{8}$ 

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