西安工程大学学报Issue(6)：821-823,3.
广义Lebesgue-Nagell方程x2-4p2r＝y3
The generalized Lebesque-Nagell equation x2 -4 p2 r= y3
摘要
Abstract
Let p be an odd prime ,using certain properties of the generalized Ramanujan-Nagell equations , the conclusion can be proved that the equation x2 -4 p2r= y3 have positive integer solutions (x ,y ,r) with gcd(x ,y)=1 if and only if p=3s2 +4 ,where s is an odd integer with s>1 .Moreover ,if the above condition holds ,then the equation has only the positive integer solution (x ,y ,r)=(s3 +12s ,s2 -4 ,1) with gcd(x ,y)=1 .关键词
广义Lebesgue-Nagell方程/正整数解/广义Ramanujan-Nagell方程Key words
generalized Lebesque-Nagell equation/generalized Ramanujan-Nagell equation/positive inte-ger solution分类
数理科学引用本文复制引用
刘妙华..广义Lebesgue-Nagell方程x2-4p2r＝y3[J].西安工程大学学报,2013,(6):821-823,3.基金项目
国家科学自然基金资助项目 （）
