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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.

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    What is a Dio-Equation? Please consider spending more time to write up your question. Your interest is what can convince people that you have thought about that question.2012-03-21
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    $ab$ could be a perfect square, and you could still have infinitely many solutions.2012-03-21
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    @Daniel, that's not in accord with Will's answer.2012-03-21
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    @GerryMyerson Sorry I didnt know that $c$ was fixed, the wording was rather confusing. I was thinking if $a=b=1$, then you could have $(x,y,c)$ being a pythagorean triple2012-03-21
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    @Daniel, OK, that clears things up. For a minute there I thought we had a proof of the inconsistency of mathematics!2012-03-21

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