纺织高校基础科学学报2016，Vol.29Issue(3)：286-290,5.DOI:10.13338/j.issn.1006-8341.2016.03.002
关于Diophantine方程组x+1=3pqa2，x2-x+1=3b2
On the system of Diophantine equations x+1=3pqa2, x 2-x+1=3b 2
摘要
Abstract
Let p,q be odd primes with 3<p<q.By using the results of quadratic and quartic Di-ophantine equations with some elementary number theory methods,it is proved that the system of equations x+1=3pqa2 ,x2-x+1=3b2 has the positive integer solution (x,a,b)=(4 367, 4,2 521)if and only if (p,q)=(7,13).关键词
Diophantine方程组/Pell方程/正整数解Key words
system of Diophantine equations/Pell's equation/positive integer solutions分类
数理科学引用本文复制引用
张小蹦,李小雪..关于Diophantine方程组x+1=3pqa2，x2-x+1=3b2[J].纺织高校基础科学学报,2016,29(3):286-290,5.基金项目
国家自然科学基金资助项目(11371291) （11371291）
陕西省教育厅专项科研计划项目(2013JK0560) （2013JK0560）
