关于Lucas猜想的推广形式

Generation of Lucas Confecture

利用初等数论方法 ,证明了丢番图方程 x(x+ 1) (2 x+ 1) =2 py2 在素数 p 1(mod8)时 ,仅有正整数解 (p,x,y) =(3,1,1) ,(3,2 4 ,70 ) ,(11,4 9,10 5) .从而 ,获得了 L ucas猜想的简洁初等证明 .同时 ,基本解决了丢番图方程 x(x+ 1) (2 x+ 1) =Dyn 的求解问题 .

By using method of elementary number theory, the authovs prove that the diophantine equation x(x+1)(2x+1)=2py 2 has positive interger solutions (p,x,y) =(3,1,1),(3,24,70) and (11,49,105) only if the prime p1(mod8), thus a concise elementary solution to lucas conjecture will be obtained;they also basically solve the diophantine equation x(x+1)(2x+1)=Dy 2 .