关于不定方程组6x^2-4y^2=2,20y^2-6z^2=14

On the Simultaneous Diophantine Equations 6x^2-4y^2=2,20y^2-6z^2=14

用初等的证明方法,即递归数列的方法,对一个不定方程组6x2-4y2=2,20y2-6z2=14进行了较深入的研究。证明了该方程组有且仅有两个正整数解,这两个正整数解分别为x(,y,z)=1(,1,1)和x(,y,z)=(89,109,199)。

In this paper, with the method of recurrence sequences, we have shown that the only two solutions in positive integers of the simultaneous Diophantine equations 6x^2-4y^2=2,20y^2-6z^2=14 are （x,y, z） = （1,1,1） and （x,y,z） = （89,109,199）.