January 7th, 2019, 12:33 PM  #1 
Newbie Joined: Dec 2018 From: england Posts: 7 Thanks: 0  Factorial problem 
January 7th, 2019, 01:11 PM  #2 
Senior Member Joined: Dec 2015 From: somewhere Posts: 514 Thanks: 80 
$\displaystyle n(!)^k $ is divisible by $\displaystyle n!$ Now just prove that $\displaystyle n(!)^k > (n!)^{(n(!)^0 1)(n(!)^1 1)...(n(!)^{k2}1)}$ 
January 15th, 2019, 05:05 AM  #3 
Senior Member Joined: Dec 2015 From: somewhere Posts: 514 Thanks: 80 
The two sides have the same elements(factors). n(!)^k has more factors , same as being greater than the left side. Proving that it can be divided by the left side is same as proving it is greater. Last edited by idontknow; January 15th, 2019 at 05:08 AM. 

Tags 
factorial, problem 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
How to prove this factorial problem?  davedave  Algebra  1  June 2nd, 2014 12:15 AM 
Problem with factorial manipulation  tonyfoster  Number Theory  1  March 24th, 2014 06:06 AM 
Inducition problem with Factorial terms  rijsthoofd  Applied Math  1  May 1st, 2010 01:03 PM 
Factorial Problem  Barbarel  Number Theory  2  August 23rd, 2009 10:08 AM 