关于不定方程组y^2-10x^2=9，z^2-17x^2=16  

On the System of Diophantine Equations y^2-10x^2=9 and z^2-17x^2=16

作　　者：马芙蓉[1] 

机构地区：[1]重庆师范大学数学与计算机科学学院,重庆400047

出　　处：《四川理工学院学报（自然科学版）》2008年第3期3-4,共2页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：重庆教委科研基金项目(010204)

摘　　要：文章运用初等证明方法,证明了标题所述的不定方程组只有x=0的整数解。从而证明了只有一个整数N=1使得1,10,17,N的任意两数之积减去1后均为平方数。In this paper, it has proved that the system of diophantine equations y^2-10x^2=9 and z^2-17x^2=16 has only integer solution x=0 by using the elementary methods.In other words, N= 1 is the only integer such that the product of any two of 1,10,17,decreased by 1 is a perfect square.

关 键 词：不定方程组 整数解 P-1集 扩张 

分 类 号：O156.1[理学—数学]