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A Method to Solve the Diophantine Equation $ax^2-by^2+c=0$

Florentin Smarandache
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Abstract

It is a generalization of Pell's equation $x^2-Dy^2=0$. Here, we show that: if our Diophantine equation has a particular integer solution and $ab$ is not a perfect square, then the equation has an infinite number of solutions; in this case we find a close expression for $(x_n,y_n)$, the general positive integer solution, by an original method. More, we generalize it for any Diophantine equation of second degree and with two unknowns $f(x,y)=0$.

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Florentin Smarandache. 2006-09-24. A Method to Solve the Diophantine Equation $ax^2-by^2+c=0$. https://arxiv.org/abs/math/0609671

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