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I am trying to find out how to solve $ax^2 - by^2 + cx - dy + e = 0$ to get integer solutions, failing this the rational solutions.


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When write the equation, the solutions will be determined by the solutions of certain equations Pell. – individ Jun 10 '14 at 5:25

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Solutions of the equation:


you can record if the root of the whole: $k=\sqrt{(c-d)^2-4q(a-b)}$

Then using the solutions of the equation Pell: $p^2-abs^2=\pm1$

Then the formula of the solution, you can write:



If the root is a need to find out if this is equivalent to the quadratic form in which the root of the whole. This is usually accomplished this replacement: $x$ in such number $x+ty$

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Forgot to say. The characters inside the brackets do not depend on the sign of the Pell equation. It depends only before $\pm{1}$ – individ Jun 10 '14 at 13:21

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