摘要
设D=2p_1…P_s(1≤s≤4),P_1…,P_s是互异的奇素数.证明了:Pell方程组x^2-3y^2=1,y^2-Dz^2=1除开D=2×7,2×3×5×7×13外,仅有平凡解(x,y,z)=(±2,±1,0).
LetD = 2p1…ps(1 〈 s 〈 4), p1,… ,ps are diverse odd primes. In this paper, the following conclusion are proved: the Pell equationsx^2 - 3y^2 = landy^2 - Dz^2 = lhas only trivial solution (x, y, z) = (±2, ±1, 0)with the exceptions that D = 2 ×7, 2 × 3 ×5 ×7 × 13.
出处
《数学的实践与认识》
北大核心
2017年第20期265-269,共5页
Mathematics in Practice and Theory
基金
江西省教育厅科学技术研究项目(GJJ160728)
云南省应用基础研究计划项目(Y0120160010)
红河学院校级教改项目(JJJG151010)
关键词
Pell方程组
基本解
整数解
奇素数
the system of Pell equations
fundamental solution
integer solution
odd prime