CAJ | 학술논문

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 x2－6 y2＝1和 y2－D z2＝4有正整数解（ x ，y ，z ）的 D 。
관우불정방정적가해성연구，시초등수론급대수수론중적중요문제。본문연구료일류이차불정방정조적가해성문제，즉：설 D시무평방인자정정수，근거Pell방정적성질，운용초등수론방법학정료소유가사방정 x2－6 y2＝1화 y2－D z2＝4유정정수해（ x ，y ，z ）적 D 。
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) .