Pell方程组x2-40y2=1与y2-Dz2=9的公解
Common solution of Pell equations x2-40y2=1 and y2-Dz2=9
贺艳峰 1韩帆 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
设D=2p1…ps(1≤s≤4),其中p1,…,ps是互不相同的奇素数.主要利用奇偶分析、同余、递归序列以及Pell方程解的性质等初等方法,对Pell方程组x2-40y2=1与y2-Dz2=9的公解进行研究.得出当D ≠ 2×7×103时,该方程组仅有平凡解(x,y,z)=(±19,±3,0);当D=2×7×103时,除了平凡解(x,y,z)=(±19,±3,0)外,还有非平凡解(x,y,z)=(±27 379,±4 329,±114).研究结果丰富了这类Pell方程组整数解的研究内容.
Abstract
Let D=2p1…ps(1≤s≤4),where p1,…,ps are distinct odd prime numbers.The common solutions of Pell equations x2-40y2=1 and y2-Dz2=9 are studied by using parity analysis,congruence,recursive sequence and properties of the solutions of Pell equations.It is concluded that when D ≠ 2×7×103,the system have only trivial solution(x,y,z)=(±19,±3,0);when D=2×7×103,in addition to the trivial solution(x,y,z)=(±19,±3,0),there is non-trivial solution(x,y,z)=(±27 379,±4 329,±114).The results enrich the research content of the integer solution of this kind of Pell equations.
关键词
Pell方程/奇偶分析/奇素数/同余Key words
Pell equation/odd and even analysis/odd prime number/congruence引用本文复制引用
出版年
2024
NETL
NSTL
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