Let m = n.
For m^n = n^m.
There are infinite solutions.
Am I missing something?
Edit: “Distinct”
Edit: “Distinct”
Adding "distinct" would have made it clearer, but it was obvious that the author meant distinct from reading the title alone.
It's math. No assumption is ever obvious. Only parts of some proofs are ever allowed to be called obvious.
Picking a mathematical formulation like you did can avoid that kind of implication, but there wasn't a template for which formulation to use and the way you wrote that makes it look like order matters which isn't right either.
And that also sounds like two ordered numbers which is not what the question calls for.