I recently started doing number theory and have finished with all the basic, intermediate and some of the advanced stuff with ease. However, I encountered this question and have been stuck for about a day with this
Solve in positive integers
I have tried modular arithematic and factorization but nothing seems to work so far. I've only been able to reduce it into an equivalent Diophantine Equation i.e.,
Further, I'm not yet acquainted with algebraic, analytic or geometric number theory, so I'd prefer an elementary solution.
Any help will be appreciated.