We need,

If,

Then,

Thus,

Thus,

The factorization of 15 is,

Examine each of the cases to get the result.

Note,

Thus, we have only two possibilities,

The equations respectively,

In each case we have,

----

If,

then,

--->Impossible.

If and

Then,

Thus,

This is a Pellian look-a-like equation.

(Now I am hoping that it has no solution to it).

I have to think about this diophantine equation.

Basically I need to show,

Has no solutions.