A quadratic diophantine equation is of form:(adsbygoogle = window.adsbygoogle || []).push({});

Ax^2 + Bxy + Cy^2 +Dx + Ey + F =0

Now, for A=0 and C=0,

Bxy + Dx + Ey + F=0 .......(1)

moreover there is one more condition, gcd(B,D,E)=1

So how do I find if some integral solution of (1) exists or not?

I am not interested in the solution itself, but rather just it's existence.

And the method must not depend on searching, as in the image here:

http://s9.postimage.org/dv30vaixb/diop.png

Original website was:

http://www.alpertron.com.ar/METHODS.HTM#SHyperb

Thanks in advance for advice and ideas.

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# Diophantine equation

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