# Need help

1. Oct 7, 2004

### Derivative86

Find all positive integers c such that it is possible to write c = a/b + b/a with positive integers a and b.

Last edited: Oct 7, 2004
2. Oct 7, 2004

### shmoe

You know $$c=\frac{a^2+b^2}{ab}$$ is an integer, so $$ab$$ divides $$a^2+b^2$$. What factors must a and b have in common?

3. Oct 7, 2004

### Derivative86

i got c=2 as the answer, is it right?

Last edited: Oct 7, 2004