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Number Theory Level pending

if x = x ! x=x! but x × y y x\times y\neq y then what is the value of x x ?


The answer is 2.

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2 solutions

Mahmod Abass
Jul 19, 2015

simply guyz there is two numbers equal their factorial values which are 1,2 and so it can't be 1 answer is 2

Pedro Souza
Jul 17, 2015

For some values of n n , we have that n ! n! is:

0 ! = 1 1 ! = 1 2 ! = 2 3 ! = 6 0! = 1 \\ 1! = 1 \\ 2! = 2 \\ 3! = 6 \\ \ldots

So we can see that, if x = x ! x = x! , then x = 1 x = 1 or 2 2 . But for x = 1 , x y = y x = 1, xy = y , with ( y 0 ) \left ( y \neq 0 \right ) .

But for x = 2 , x y = 2 y x = 2, xy = 2y , again with ( y 0 ) \left ( y \neq 0 \right ) .

So, the correct answer is x = 2 x = 2 .

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