Factorial of Smallest Multiple Divisible by Square! V-002
Find the smallest positive integer value such that for every positive integer greater than 1, is divisible by , but not by .
If there is no such positive integer value , then enter 0.
The answer is 0.
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.
1 solution
Fact-1: One can see that for every natural number n , ( n × n ) ! = ( n 2 ) ! is divisible by n 3 .
Fact-2: x m i n = 1 doesn't work.
Whatever value you try to assign to x m i n > 1 , let it be y , when a will assume the same value and it surely will, ( x a ) ! will be then equal to ( a 2 ) ! and, by Fact-1 , be divided by ( a 3 ) .
So, such x m i n doesn't exist.
Hence, the answer is 0 .