Is the set of $n,m$ s.t. $2^n-3^m=1$ or $3^m-2^n=1$ finite? tried factoring but got nowhere, not sure what theorem or subject applies to this question.
PS : no it is not a homework, but if a book has this as homework please give a reference.
Tagging as possible elementary-number-theory , modify if incorrect
It is not just finite, it is a singleton. There is a much stronger property:
https://en.wikipedia.org/wiki/Catalan%27s_conjecture