I have this problem: Ax^2 + Cy^2 + Dx + Ey + F = 0, (B = 0 => Bxy)
I need to know under which circumstances the above has solution(s). Thank you for your time.
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1$\begingroup$ What kind of solution? Complex numbers (always), real numbers (depends on the discriminant), rational numbers (there are theorems that will help you here), etc. In any case, this belongs on MathStackExchange, not MathOverflow. $\endgroup$– Joe SilvermanCommented Jun 7, 2016 at 13:55
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$\begingroup$ I am more interested in N numbers. But solutions in Q could help me as well. $\endgroup$– DK485Commented Jun 7, 2016 at 14:04
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$\begingroup$ which theorems are you referring to? Is there a good book that could help me? $\endgroup$– DK485Commented Jun 7, 2016 at 14:09
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1$\begingroup$ Possible duplicate of Is there an algorithm to solve quadratic Diophantine equations? $\endgroup$– Stefan Kohl ♦Commented Jun 7, 2016 at 14:50
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$\begingroup$ @DK485 A quadratic equation has a solution in $\mathbb Q$ if and only if it has solutions in $\mathbb Q_p$ for all $p$ and in $\mathbb R$. $\endgroup$– Joe SilvermanCommented Jun 7, 2016 at 17:31
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