关于不定方程组9x^2－7y^2＝2，32y^2－9z^2＝23

ON THE SYSTEM OF DIOPHANTINE EQUATIONS 9x￣2-7y￣2= 2, 32y￣2- 9z￣2 =23

利用不定方程ｘ２－Ｄｙ２＝Ｃ（Ｄ∈Ｎ，Ｃ∈Ｚ－｛０｝）的整数解的结构，给出了不定方程组９ｘ２－７ｙ２＝２，３２ｙ２－９ｚ２＝２３的所有正整数解的一个表达式．由这个表达式，经过初等计算。

By the structure of integer solutions of the diophantine equation x2-Dy2=C (D ∈ N, C ∈Z - {0} ), this paper gives an expression of the positive integer solutions of the system of diophantine equations 9x2-7y2=2, 32y2-9z2=23.According to the expression, one can obtain the positive integer solutions of this system of diophantine equations by elementary calculating.