1. the factoring method
Solution: , so .
Considering the positive divisors of we obtain:
yielding the solutions (writing ):
, , , ,
and their equivalents with and swapped. And the special case:
with the solution , i.e. 9 solutions in all.
where , has solutions in positive integers.
The equation is equivalent to and has positive divisors.
(to be continued)
Andreescu, Andrica, Cucurezeanu – An Introduction to Diophantine Equations