1. the factoring method
Solve in positive integers
, where
and
are prime.
Solution:
, so
.



Solution:


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)
further reading
Andreescu, Andrica, Cucurezeanu – An Introduction to Diophantine Equations