不定方程x^3+1=Dy^2的参数解  

On the Parametric Solutions of the Diophantine Equation x^3+1=Dy^2

作　　者：杨雅琴[1] 

机构地区：[1]齐齐哈尔大学理学院,黑龙江齐齐哈尔161006

出　　处：《内江师范学院学报》2016年第4期1-4,共4页Journal of Neijiang Normal University

摘　　要：利用参数法将不定方程x^3+1=Dy^2(D>0)分解成一个一元一次方程和一个一元二次方程组成的方程组,对这个方程组的解用参数表示,通过设定此参数的值来得到该不定方程的非平凡解.首先讨论D不可约时,不定方程x^3+1=Dy^2(D>0)非平凡解的求解方法,其后给出一些不同D值对应的不定方程x^3+1=Dy^2(D>0)的非平凡解,最后讨论D可约时,不定方程x^3+1=Dy^2(D>0)非平凡解的求解方法,也给出了相应的不定方程的非平凡解.By use of the parameter method,x^3 ＋1= Dy^2（D 0）is decomposed into an equation set composed of a one degree equation and a quadratic equation,whose solutions are expressed by aparameter,and by giving this parameter a value,the nontrivial solutions of this indeterminate equation are thus obtained.This article first discusses the ways for determining the solutions of x^3＋1= Dy^2（D 0）when Dis Irreducible.Then the correspondent nontrivial solutions of x^3＋1=Dy^2（D 0）are presented when the value of Dis different.Finally ways for determining the non-trivial solutions for x^3＋1= Dy^2（D 0）are examined when Dis reducible,and the non-trivial solutions for the correspondent indeterminate equations are also put forth.

关 键 词：参数法 不定方程 非平凡解 构建 

分 类 号：O156.1[理学—数学]