Pell方程组x2-33y2=1与y2-Dz2=16的公解
On the common solution of Pell equations x2-33y2=1 and y2-Dz2=16
韩帆 1贺艳峰 1李勰1
作者信息
- 1. 延安大学数学与计算机科学学院,陕西延安 716000
- 折叠
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x2-33y2=1与y2-Dz2=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.
Abstract
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 x2-33y2=1 and y2-Dz2=16 was studied when D=2p1…ps(1 ≤s≤4),where p1,…,ps were different odd prime numbers.In 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Key words
Pell equation/common solution/odd and even analysis/odd prime number/congruence引用本文复制引用
基金项目
国家自然科学基金(12261090)
国家自然科学基金(11961072)
延安大学校级科研项目(YDJGYB21-26)
出版年
2024
NETL
NSTL
万方数据