Unique factorial
We know that ( n ! ) ! = n ! ( n ! − 1 ) ! .
However, there exists one unique solution to c ! = a ! b ! , where a , b , and c are distinct natural numbers. Then, find the value of c + a + b .
Warning: be cautious before entering your answer. Cross check that your answer is not of the mentioned form ( n ! ) ! = n ! ( n ! − 1 ) !
The answer is 23.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
2 solutions
Fermat's library, I guess?
@Adhiraj Dutta , you have to mention that a , b , and c are distinct natural numbers. If not, ( a , b , c ) = ( 1 , 1 , 1 ) and ( 1 , 2 , 2 ) are also solutions.
The answer is not unique. a = 5 , b = 3 , c = 6 also satisfy the equation.
Log in to reply
You're flawed in your judgement, as that is only equivalent to ( n ! ) ! = n ! ( n − 1 ) ! with n = 3 . This has been clearly stated as having infinite solutions.
Log in to reply
yeah, he is flawed in his judgment. What kinda language is that?
Log in to reply
@Alexander Shannon – I'm sorry? What do you mean? I don't quite understand.
Log in to reply
@Adhiraj Dutta – Sorry, I was sleep-writing again last night :D
Log in to reply
@Alexander Shannon – What's that haha
@Alexander Shannon – What is wrong in my statement ?
Log in to reply
@Shikhar Srivastava – Sorry, I was sleep-writing again last night :D
Luckily i had seen that 1 0 ! = 6 ! 7 ! ⟹ a + b + c = 2 3