- #1
sparsh12
- 12
- 0
A quadratic diophantine equation is of form:
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.
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.