On the diophantine equation X^2-(1+a^2)Y^4 =-2a  

作　　者：YUAN PingZhi 1 & ZHANG ZhongFeng 2 1 School of Mathematics,South China Normal University,Guangzhou 510631,China 2 School of Mathematics & Computational Science,Sun Yat-Sen University,Guangzhou 510275,China 

出　　处：《Science China Mathematics》2010年第8期2143-2158,共16页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.10971072);Guangdong Provincial Natural Science Foundation (Grant No.8151027501000114)

摘　　要：Let a≥1 be an integer.In this paper,we will prove the equation in the title has at most three positive integer solutions.Let a≥1 be an integer.In this paper,we will prove the equation in the title has at most three positive integer solutions.

关 键 词：algebraic APPROXIMATIONS continued FRACTIONS ELLIPTIC curves QUARTIC equations 

分 类 号：O175[理学—数学]