Pell方程组x^(2)-33y^(2)=1与y^(2)-Dz^(2)=16的公解  

On the common solution of Pell equations x^(2)-33y^(2)=1andy^(2)-Dz^(2)=16

作　　者：韩帆 贺艳峰[1] 李勰 HAN Fan;HE Yan-feng;LI Xie(School of Mathematics and Computer Science,Yan’an University,Yan’an 716000,China)

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《西南民族大学学报（自然科学版）》2024年第3期347-354,共8页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：国家自然科学基金项目(12261090,11961072);延安大学校级科研项目(YDJGYB21⁃26)。

摘　　要：利用奇偶分析、递归序列、同余和Pell方程的解的性质等一些初等方法,对D=2p1……ps(1≤s≤4),其中p1,…,ps是互不相同的奇素数时,Pell方程组x^(2)-33y^(2)=1与y^(2)-Dz^(2)=16的公解进行了研究.得到除开D=2×7×151,方程组有非平凡解(x,y,z)=(±48599,±8460,±184)这一基本情况之外,仅有平凡解(x,y,z)=(±23,±4,0),从而推进了这类Pell方程组整数解的研究.By using some elementary methods such as parity analysis,recursive sequence,congruence and properties of Pell e⁃quation solutions,the common solutions of the equations x^(2)-33y^(2)=1andy^(2)-Dz^(2)=16 was studied when D=2p1…ps(1≤s≤4),where p1…ps,were different odd prime numbersIn addition to the basic case that D=2×7×151 had a non⁃trivial solution(x,y,z)=(±48599,±8460,±184),there was only one trivial solution(x,y,z)=(±23,±4,0),thus advancing the study of integer solutions of this kind of Pell equations.

关 键 词：PELL方程 公解 奇偶分析 奇素数 同余 

分 类 号：O156[理学—数学]