Find all positive numbers N with the following property: The greatest factor of N (other than N) is 6 times the smallest divisor of N (other than 1).
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;
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.