My Math Forum Factorial problem

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 January 7th, 2019, 12:33 PM #1 Newbie   Joined: Dec 2018 From: england Posts: 7 Thanks: 0 Factorial problem Could someone please help me ?
 January 7th, 2019, 01:11 PM #2 Senior Member   Joined: Dec 2015 From: somewhere Posts: 636 Thanks: 91 $\displaystyle n(!)^k$ is divisible by $\displaystyle n!$ Now just prove that $\displaystyle n(!)^k > (n!)^{(n(!)^0 -1)(n(!)^1 -1)...(n(!)^{k-2}-1)}$
 January 15th, 2019, 05:05 AM #3 Senior Member   Joined: Dec 2015 From: somewhere Posts: 636 Thanks: 91 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.

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