关于Pell方程x^2-18y^2=1与y^2-Pz^2=16公解的研究  

Common Solution to Pell Equations x^2-18y^2=1 and y^2-Pz^2=16

作　　者：赵建红 

机构地区：[1]丽江师范高等专科学校数学与计算机科学系,云南丽江674199

出　　处：《河北北方学院学报（自然科学版）》2017年第1期1-4,共4页Journal of Hebei North University:Natural Science Edition

基　　金：云南省教育厅科研基金项目(2014Y462);红河学院校级课题(XJ15Y22)

摘　　要：目的 Pell方程的公解是数论中的一个重要问题。设P=2p_1…ps(1≤s≤4),p_1,…,ps(1≤s≤4)是互异的奇素数,关于Pell方程组x^2-18y^2=1与y^2-Pz^2=16的整数解的初等解法至今仍未解决。方法主要利用同余的性质、Pell方程解的性质和递归序列等方法。结果得出Pell方程组x^2-18y^2=1与y^2-Pz^2=16仅当D=2×577时有非平凡公解(x,y,z)=(±19601,±4620,±136)。结论推进了该类Pell方程组整数解的研究。Objective The common solution to Pell equations is a very important problem of Number theory.Let P=2p_1…ps(1≤s≤4),where ps(1≤s≤4)are distinct odd primes,the common solution to Pell equations of x^2-18y^2=1 and y^2-Pz^2=16 still remains unresolved.Methods Congruence,some properties of the solutions to Pell equation and recursive sequence were used.Result The Pell equations in the title have two nontrival common solutions only when D=2×577.Conclusion These results promote the study of the kind of Pell equations.

关 键 词：PELL方程 公解 整数解 同余 递归序列 

分 类 号：O156[理学—数学]