# solving diophantine equations

1. the factoring method

Solve in positive integers , where and are prime.
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)