关于不定方程组x^2-5y^2=1与y^2-Dz^2=16的公解  

On the Simultaneous Diophantine Equations x^2-5y^2=1 and y^2-Dz^2=16

作　　者：万飞[1] 杜先存[1] 

机构地区：[1]红河学院教师教育学院,云南蒙自661199

出　　处：《重庆师范大学学报（自然科学版）》2016年第4期105-109,共5页Journal of Chongqing Normal University:Natural Science

基　　金：云南省教育厅科研基金(No.2014Y462);红河学院校级课题(No.XJ15Y22);红河学院中青年学术骨干培养资助项目(No.2015GG0207)

摘　　要：运用Pell方程的解的性质、递归序列和同余等初等方法讨论了当p_s(1≤s≤4)是互异的奇素数,D=2~tp_1^(a1)p_2^(a2)·p_3^(a3)p_4^(a4)(ai=0或1,1≤i≤4,t∈Z^+,且t≠2,4)时,不定方程组x^2-5y^2=1与y^2-Dz^2=16仅当D=2t×7×23(t=1,3,5,7)时有正整数解。Let D=2^t p1^a1p2^a2·p3^a3p4^a4（ai=0 or 1,1≤i≤4,t∈Z^＋,and t≠2,4）, where ps（1≤s≤4）are distinct odd primes, the simul- taneous Diophantine equations in the title has a positive integer solution only when D==2^t×7×23（t=1,3,5,7）are discussed with the help of some properties of the solutions to Pell equation, recursive sequence and congruence.

关 键 词：不定方程组 整数解 奇素数 递归序列 

分 类 号：O156[理学—数学]