更新时间：08-03 （徐冬冬）提供原创文章
摘要:关于Pell方程的相关理论前人已经有了很多的研究，但是在其具体的解题方法上还存在着解法单一或者找不到解题方法的问题，为了解决这一问题。本文主要以x2-Dy2=C型的Pell方程的整数解的求解方法为研究对象。通过对其基本解的探讨，归纳出几种求解Pell方程x2-Dy2=C的整数解的方法，包括同余法、连分数法、变换法、矩阵法和公式法，其中公式法是本文研究得出的一种新方法。本文中应用上述的一些方法对具体的问题进行求解，希望最终能够实现一题多解，解法多样化的目的。
关键词： Pell方程；基本解；整数解
ABSTRACT:There were lots of researches about the theories related to Pell equation, however, when it comes to the specific solution methods, it still exists the problems of single solution and finding no solution method. In order to solve these problems, this paper focused on to research the methods of solving the Integer solution of the x2-Dy2=C typed Pell equation. Basing on the fundamental solution, we had summarized several solution methods of the Integer solution of Pell equation x2-Dy2=C, including the congruence, continued fraction method, variation method, the matrix method and the formula method, in which the formula method proposed in this paper is a new method. This paper had used some of the above method to deal with the specific problems, hoping to be able to achieve the goal of several solutions to one problem, and the diversification of the solutions ultimately.
Keywords: Pell equation; fundamental solution; integer solution