Is This Another Factorials Identity?

Number Theory Level 1

True or false :

$\Large (n!)! = n! \times (n!-1)!$

True False

4 solutions

A Former Brilliant Member
Mar 18, 2016

Let $n!=m$ . The expression is equivalent to $m!=m(m-1)!$ which is true.

I have made the substitution just to make it more clear.

Yes! It is just that simple!

Chung Kevin - 5 years, 2 months ago

Same method !

Chirayu Bhardwaj - 5 years, 2 months ago

It's not true for n=0,1 so please make it clear

Shiv Kumar - 5 years, 2 months ago

Why so, $(0!)! = 0! × (0!-1)!$
$1 = 1 ×(1-1)!$
$1 = 1×0!$
$1=1×1$
$1=1$ .

Ashish Menon - 5 years, 2 months ago

I can't see last factorial symbol. Your solution is right. Thanks for clarifying

Shiv Kumar - 5 years, 2 months ago

@Shiv Kumar – Which last factorial? Thanks :-)

Ashish Menon - 5 years, 2 months ago

It is true. 0!=1.

A Former Brilliant Member - 5 years, 2 months ago

Suzie Nguyen
Jun 4, 2021

I guessed ;))

Aiman Aimn
Mar 23, 2016

n! Exactly

Calvin Rieder
Mar 23, 2016

Let n!=x

x! = x*(x-1)!

x! = x*(x!/x)

x! = x!