The Diophantine equation of the form a$x^2$ – b$y^2$ = $c^2$ with ab is not a perfect square in Z has infinitely solutions in N, provided by a particular non-trivial solution in set of N.
I have racked my brains trying to think why ab not a perfect square should invalidate the proof, but can't think why. I have many books on number theory, but none have an equation like this.
If any one can help me in this aspect...I am so thankful to them.