关于不定方程组x^2-18y^2=1与y^2-bz^2=16的公解  

On the common solution of the simultaneous diophantine equations x^2-18y^2=1 and y^2-bz^2=16

作　　者：瞿云云 QU Yun-yun(School of Mathematical Sciences,Guizhou Normal University,Guiyang 550001,China)

机构地区：[1]贵州师范大学数学科学学院,贵州贵阳550001

出　　处：《东北师大学报（自然科学版）》2020年第4期1-5,共5页Journal of Northeast Normal University(Natural Science Edition)

基　　金：贵州省科学技术基金资助项目(黔科合基础[2019]1221号).

摘　　要：利用初等数论的方法研究了不定方程组x^2-18y^2=1与y^2-bz^2=16的公解问题,得到了当b=p(p为任意素数)与b=pq(p<q,p,q为任意两个不相同的素数)时,方程组的解.By using some elementary number theory methods,the common solutions of the simultaneous diophantine equations x^2-18 y^2=1 and y^2-bz^2=16 are given in the case of b=p(pis a prime)and b=pq(p,q are distinct primes and p<q).

关 键 词：不定方程组 PELL方程 整数解 

分 类 号：O156[理学—数学]