1. ## No. of solutions..

how many solutions are there in N*N to the equation 1/x + 1/y = 1/1995 ?

2. I am afraid that it is not correct

$(x-1995)(y-1995) = -1995(x+y) + xy + 1995^2$

and $1995^2 = 3^2 \cdot 5^2 \cdot 7^2 \cdot 19^2$

3. Well, let me try again:

Attempt #2:

$\frac1{x} + \frac1{y} = \frac1{1995} \Leftrightarrow (x - 1995)(y - 1995) = 1995^2 = 3^2 5^2 7^2 19^2$

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.