Need help

[Derivative86]

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

[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?

[Derivative86]

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