求解丢番图方程$ax^2-by^2+c=0$的一种方法
A Method to Solve the Diophantine Equation $ax^2-by^2+c=0$
摘要：
它是Pell方程$x^2-Dy^2=0$的推广。在这里，我们表明：如果我们的丢番图方程有一个特定的整数解，而$ab$不是一个完满平方，那么这个方程有无穷多个解;在这种情况下，我们用一种原始的方法找到了一般正整数解$(x_n,y_n)$的一个封闭表达式。进一步，我们将它推广到任何二次丢番图方程和两个未知数$f(x,y)=0$ .
英文摘要：
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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