中文摘要：

关于不定方程的可解性研究,是初等数论及代数数论中的重要问题.本文研究了一类二次不定方程组的可解性问题,即:设D是无平方因子正整数,根据Pell方程的性质,运用初等数论方法确定了所有可使方程x2-6y2=1和y2-Dz2=4有正整数解(x,y,z)的D.

英文摘要：

The study of solvability of the Diophantine equation is one of the most important problems in elementary number theory and algebraic number theory .The solvability of a class of system of quadratic Diophantine equations is studied .That is ,let D be a positive integer with square free ,using elementary number theory methods with some properties of Pell equations ,it is determined that all D w hich make the system of Diophantine equations x2 -6 y2 =1 and y2 -Dz2 =4 has positive integer solutions (x ,y ,z) .