Critical factorials

How many integers n n satisfy

( ( ( ( ( n ! ) ! ) ! ) ! ) ! ) ) ! = n ? (((((n!)!)!)!)!)\ldots)!=n ?

3 infinite solutions 6 4 2 0 5 1

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2 solutions

Sudoku Subbu
Jan 30, 2015

There exists two solutions because (((((1!)!)!)!)!)!..............)!=1 and also (((((2!)!)!)!)!)!)...........)! = 2 that's it

Disturbed by what told me that the question is having problem. Did not think of simple but others. At least two but I answered 1.

Lu Chee Ket - 6 years, 4 months ago

I was confused by the dispute, and didn't check that the equation did not have a ! a the end.

The answer 2 is correct. Sorry to those who had their answer marked wrong and then correct.

Calvin Lin Staff - 6 years, 4 months ago

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is'nt this problem interesting

sudoku subbu - 6 years, 4 months ago
. .
Mar 15, 2021

Only 0 0 , and 1 1 satisfy the equation.

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