关于丢番图方程X^5±X^3=Dy^3

On the Diophantine Equations X^5 ± X^3 = DY^3

利用数论方法获得了丢番图方程x5-x3 =Dy3 有正整数解的充要条件 ,证明了当p为素数时 ,方程在D =P≡ 3 ,5 (mod9)时 ,仅有正整数解 (p ,x ,y) =(3 ,2 ,2 ) ,(3 ,5 ,10 ) ;在D =2P ,p≡ 2 ,3 (mod9)时 ,仅有正整数解 (p ,x ,y) =(3 ,7,14 ) ;在D =4P ,p≡ 2 ,3 ,5 (mod6)时 ,仅有正整数解 (p ,x ,y) =(2 ,3 ,3 ) ,(17,1163 ,14 695 3 8)。

With the help of the theory of number, this dissertation shows that the Diophantine Equations X 5 ± X 3=DY 3 has integer solutions when D=P≡3,5(mod9), D=2P≡2,3(mod9) and D=4P≡2,3,5(mod6).