Why are these being answered...I thought it was forbidden to post "contest" problems here.
Not only that, but Kanwar shows no work....
Up to 10000 the only number with such property is 24 .
Small Maple program :
Code:for N from 1 to 10000 do for i from 2 to N do if N mod i = 0 then a:=i: break; end if; end do; for j from N-1 to 2 by -1 do if N mod j = 0 then b:=j: break; end if; end do; if b=6*a then print(N); end if; end do;
Well, since no moderator has jumped in with the eviction papers, looks like that
rule has now been abolished....so:
u = greatest factor, v = lowest factor
If N is even, then no choice: v = 2 and u = N/2
So N/2 = 6v
N/2 = 12
N = 24
If N is odd, then u and v will be odd
But 6*(odd number) = even
So none if N is odd.
Heretoforth, henceforth and allforths, only N=24 is solution.