The problem goes like this

for what integral value of n will the expression

2*n / (n-4) be a positive integer.

obviously the n must be greater than 4

and we can show that the expression is integer for
n = 5, 6, 8, 12

however, how do we prove that no n from 13 and onwards will give the expression an integral value?

2n / (n-4) = 2 + 8 / (n-4)

So we see that this can only be an integer if (n-4) is a factor of 8, and furthermore, it is only a positive integer if 8/(n-4) is greater than or equal to -1.

The factors of 8 are 1,2,4,8 (and -1,-2,-4,-8 for our purposes)

so n = -4,5,6,8,12

> obviously the n must be greater than 4

be careful with what is 'obvious'

Rich