不定方程x^2-Dy^2=z^2(D＞0)的参数解  

Solution of Parameters on the Diophantine Equation X^2-Dy^2=Z^2(D＞0)

作　　者：杨雅琴[1] 

机构地区：[1]齐齐哈尔大学理学院

出　　处：《科技通报》2018年第10期17-19,38,共4页Bulletin of Science and Technology

基　　金：黑龙江省教育厅基本业务专项(135109232)

摘　　要：利用参数法给出不定方程x^2-Dy^2=z^2(D> 0)非平凡解的参数形式以及解的一些性质,研究了不定方程x^2-aby^2=1(ab> 0)非平凡解的参数形式,最后给出了不定方程ax^2-by^2=z^2(a> 0,b> 0)非平凡解的参数形式,以及不定方程ax^2-by^2=1(a> 0,b> 0)非平凡解的参数形式。Using the method of parameter diophantine equation x^2-Dy^2=z^2(D>0) is given The parameters of nontrivial solution form and some properties of solutions. Diophantine equation x^2-aby^2=1(ab>0) is studied the parameters of nontrivial solution form, In the end, the indefinite equation ax^2-by^2=z^2(a>0,b>0) was presented nontrivial solution form of parameters, and the in determinate equation ax^2-by^2=1(a>0,b>0)the parameters of nontrivial solution form.

关 键 词：参数法 不定方程 非平凡解 

分 类 号：O1[理学—数学]