关于Eisenstein数的Terai猜想(英文)  

On Terai' s conjecture concerning Eisenstein numbers

作　　者：乐茂华[1] 

机构地区：[1]湛江师范学院数学系,广东湛江524048

出　　处：《纺织高校基础科学学报》2003年第4期281-283,共3页Basic Sciences Journal of Textile Universities

基　　金：The national natural,science foundation of China(10271104);the guangdong provincial natural science foundation(011781);the natural science foundation of the education department of guangdong province(0161)

摘　　要：设(a,b,c)是一组Eisenstein数,证明了:当2|ab且c是素数方幂时,方程a2x+axby+b2y=cz仅有正 整数解(x,y,z)=(1,1,2).Let (a,b,c) be an Eisenstein triple. It is proved that if 2 |ab and c is a prime power,then the equation a2x+axby+b2y=cz has only the positive integer solution (x,y,z)=(1,1,2).

关 键 词：纯指数DIOPHANTINE方程 Eisenstein数 TERAI猜想 

分 类 号：O156[理学—数学]