Think Logically not mathematically [part-37]

Number Theory Level 2

How many values exist such that $(((((n!)!)!)!)!)\ldots)!=n ?$

3 2 0 5 6 7 1 4

1 solution

Viki Zeta
Jun 30, 2016

$n! = n\text{, for all n } \in {2, 1}\\ \text{So it takes up 2 values}$

What about 2!? 2!=2 so applying factorial infinite times it will still be 2.

Damien Ashwood - 4 years, 11 months ago

Yes, it works for 2. It does not work for 0. So, the final answer is srill 2 that is for 1 and 2.

Ashish Menon - 4 years, 11 months ago

Yeah. Updated!

Viki Zeta - 4 years, 11 months ago

Hey vicky, maybe your answer is wrong it does not work for 0, it gives 1, it works only for 1 and 2

Ashish Menon - 4 years, 11 months ago

Correct. @soduku subbu what are the infinite parentheses for?

Ashish Menon - 4 years, 11 months ago

Maybe possibly many $n!$ occur infinitely.

Viki Zeta - 4 years, 11 months ago

Yh, but there are no alternating factorials and parentheses, they are only parentheses.

Ashish Menon - 4 years, 11 months ago

@Ashish Menon – As far as I think, he is meaning many brackets $( )$ LOL

Viki Zeta - 4 years, 11 months ago