关于一个不定方程组正整数解的上界  

On the Upper Bound for the Positive Integer Solutions of the System of Diophantine Equations

作　　者：贺腊荣[1] 

机构地区：[1]西北大学数学系,西安710127

出　　处：《四川理工学院学报（自然科学版）》2011年第1期34-37,共4页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

摘　　要：运用Baker方法得到不定方程组13x2-11y2=2,48x2-13z2=35正整数解的上界,即记S={(x,y,z)|x,y,z∈Z,并且满足方程组13x2-11y2=2,48x2-13z2=35},T={y|(x,y,z)∈S}若能求得T的上界,只要将解内的y值代入方程组,就可求得方程组的全部正整数解。可以得到上界方程组13x2-11y2=2,48x2-13z2=35的上界为(x,y,z)=(0.92×2418393,2418393,1.92×2418393)。By Baker＇ s method, this paper solutes the upper bound for the positive integer solution of the system of Dio-phantine equations 13x^2-11y^2=2,48x^2-13z^2=35, was soluted and letS = { （x, y, z） ｜ x, y, z ∈ Z, and, 13x^2-11y^2=2, 48x^2-13z^2=35, T = ｜y｜ （x, y, z） ∈ S} , If we can get the upper bounds of T and as long as we let y of solution put the system of Diophantine equations, we may get all integer solutions of the system of Diophantine equations and we can get the upper bounds are （x,y,z） = （0.92×24^18^m,24^18^m,1.92×24^18^m）

关 键 词：不定方程组 解的上界 BAKER方法 

分 类 号：O156[理学—数学]