For $n$ and $m$ strictly positive integers with $n \ne m$, I guess that $x^m - y^n$ is irreducible in any field, but I am not sure. In particular, I have no idea how this could be proved. My question is thus:

- Is $x^m - y^m$ irreducible ? In any field, or only in fields with some restriction?
- If yes, how to prove it ? If no, is there a concrete counterexample?