关于Diophantine方程x^3-1=3py^2

On the Diophantine Equation x^3-1 =3py^2

利用同余及勒让德符号的性质等初等数论的方法,得到了丢番图方程x3-1=3py2无正整数解的4个充分条件,推进了该类三次丢番图方程的研究。

Let p be an odd prime,the positive integer solutions situation of the Diophantine equation x3 -1 = 3py2 is studied. Using elementary theory of numbers methods,some sufficient conditions that the Diophantine equation has no integer solution has been proved.