有限简单连分数的逼近原理在Pell方程上的应用

Approximation Principle of Finite Simple Continued Fractions to Pell Equation

形如x^(2)-dy^(2)=±1的不定方程即Pell方程,用初等方法难以求解,解析其解的构造更加困难.运用有限简单连分数的独特性质,用逼近原理来探讨两类Pell方程的解法及其解的关系,从理论上阐述了用逼近原理解Pell方程的有效性,并为研究这类不定方程解的构造提供一个简洁而实用的方法.

The Pell equation,an indefinite equation in shape[x^(2)-dy^(2)=±1],is difficult to solve by elementary method,and the construction of analytical solution is more difficult. This paper uses the unique properties of finite simple continued fraction and the approximation principle to explore the solution of two kinds of the Pell equations and the relationship between their solutions. It expounds the effectiveness of using the approximation principle to solve the Pell equations,and provides a concise and practical method for studying the construction of solutions of this kind of indefinite equations.