一类不定方程的整数解

The Integral Solutions to a Kind of System of Diophantos'Equations

本文在整数范围内讨论文中（１）所示的一类不定方程．首先我们给出这类方程的解的一些基本性质；其次分别给出方程Ｅ（２，２）、Ｅ（２，３）及Ｅ（３，３）的通解，然后我们用递归的方法刻划Ｅ（ｍ，ｎ）的解集Ｓ（ｍ，ｎ）的结构；最后给出求解方程Ｅ（ｍ，ｎ）的一种算法．

In this paper a kind of system of Diophantos'equations of the type as theformula (1) in the text is studied.First,the properties of solutions of thiskind of ystems are stated.Then the general solutions of systems E(2,2),E(2,3),E(3,3)are given.Fartheremore,the construction of the set of solutions S(m,n) of system E (m,n)is discussed by the recurrent method. Finally,an arithmetic of solving the system E(m,n)is abtained.