求一类不定方程x^(2)+y^(2)=z^(m)的正整数解

Finding Positive Integer Solutions of a Class of Indefinite Equations

应用勾股数原理给出了求不定方程x^(2)+y^(2)=z^(2^(n))正整数解的一种迭代计算法,通过先导出满足该方程的迭代计算方法,然后根据求解需要赋予某初始值代入迭代公式计算,从而求得满足该不定方程的某一组正整数解.同时应用本方法进一步解决了一类不定方程x^(2)+y^(2)=z^(m)(m为正整数)的求解问题.

This paper presents an iterative method for finding positive integer solutions of indefinite equations by using Pythagorean number principle.The method is to first derive a regular iterative formula of the equation,and then assign a certain value to the iterative formula to calculate in turn,so as to obtain the positive integer solution of the indefinite equation.Furthermore,the calculation method for the positive integer solution of a class of indefinite equation is obtained by using the iterative method.