关于不定方程组11x^2-9y^2=2,40y^2-11z^2=29

On the System of Diophantine Equations 11x^2-9y^2 =2 and 40y^211z^2=29

对于不定方程组a2x2-a1y2=a2-a1,a3y2-a2z2=a3-a2,本文取(a1,a2,a3)=(9,11,40),得不定方程组 11x2-9y2=2,40y2-11z2=29。再进一步构造出一个集合M,M中的数由一个二无线性递归数列确定,在此基础上做一些初等计算,即可求出本文所得的不定方程组的解。

This paper discusses the system of diophantine equations 11x^2 -gy^2 =2 and 40y^2 -11z^2 =29,and gives a method of the positive integer solution.