Number of integer solutions of $\frac{1}{x} + \frac{1}{y} = \frac{1}{1000}$ What is the number of integer solutions of:
$$\frac{1}{x} + \frac{1}{y} = \frac{1}{1000}$$
How to solve these type of problems if am comfortable of solving $x+y=z$. But how to do if multiplicative inverses are involved?

Assuming you mean integer solutions, you will be able to rewrite your equation as:
$1000(x+y) = xy$
Then rearranging you will be able to write as:
$(x - 1000)(y - 1000) = 1000^2$
So that your solutions for $x-1000$ and $y-1000$ correspond to divisors of $1000^2$. 
