This seems odd,
If I write my two rational numbers
in reduced form as
then there's a problem (one I'm certain is a consequence of GauÃŸ' lemma, but am too lazy to check).
since we're dealing with the positive integers, we can assume the raising to the
Then I raise both sides to the
as that clearly gives a trivial result)
, so this means that our fraction is also a natural number. But then as we chose
reduced, this implies
was secretly a positive integer named
in the first place.
The argument is symmetric in showing
, so there are no extra rational answers, only the integer ones.