how many solutions are there in N*N to the equation 1/x + 1/y = 1/1995 ?
Well, let me try again:
Attempt #2:
$\displaystyle \frac1{x} + \frac1{y} = \frac1{1995} \Leftrightarrow (x - 1995)(y - 1995) = 1995^2 = 3^2 5^2 7^2 19^2$
We observe that if x - 1995 is negative then y - 1995 will also be. But at least one of the factors has to less than -1995, giving us negative solutions, which we do not want.
Thus both x - 1995 and y - 1995 are positive.
Since we have 81 factors for 1995^2 ,we have 81 solutions for x,y.