After alexmahone's and CaptainBlack's excellent work on a previous problem
I've worked myself into another corner.
Tackling this equation
with the same method as the previous post, this time using and as factors of , I ended up with the result I was expecting but hoping against.
I want results other that the trivial and
I don't think that and can be positive integers and satisfy this equation, but , and certainly can.
When , , , and then
I tried using the quadratic formula, solving first for , then substituting this value back in and solving for .
This only led to
Not much help then.
I've tried different ways for getting the difference of squares
but these lead to incorrect results.
How can I calculate the relationship between p, q, r and s?