Find all pairs of $(m, n)$ where $m, n \in \mathbb Z$ for which $m/n + n/m$ is an integer. Find all pairs of $(m, n)$ where $m, n \in \mathbb Z$ for which $m/n + n/m$ is an integer.

Clearly one can find $m, n = +1$, or $- 1$. But are there any other solutions. Any help is appreciated? 

Hint:
For $m = n$ , the condition is always True.
Consider  $ m \ne n $ such that : $$\frac mn =  x \text{ and  } \frac nm = y \space \space $$
Then $$\frac1x +  x = n \space \space \text{ such that } n\in \mathbb Z$$
Can you find the values of $x$ for which $\frac1x + x $ is an integer?
