## A Method to Solve the Diophantine Equation a X^{2}-B Y^{2} + C = 0

**Authors:** Florentin Smarandache

We consider the equation
(1) ax^{2} - by^{2} + c = 0, with a,b ε N* and c ε Z*.
It is a generalization of Pell's equation: x^{2} -Dy^{2} = 1. Here,
we show that: if the equation has an integer solution and a.b is
not a perfect square, then (1) has an infinitude of integer
solutions; in this case we find a closed 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.

**Comments:**
10 pages.

**Download:** **PDF**

### Submission history

[v1] 13 Mar 2010

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