关于不定方程x^3=Dy^2+1

On The Diophantine Equation x 3=Dy 2+1

本文对方程x3=Dy2+1中一般情形的D进行了讨论,对0<D<100且D不含平方因子,不定方程x3=Dy2+1,仅当D=7,26,31,38,61时,有非平凡解,而对于D=7,26,31,38和61时。

In this paper,we study the equation of the title with D general. The equation has nontrivial integer solutions, only when D =7, 26, 31, 38 or 61, for 0<D<100 and squarefree. We have got some solutions of the equation of the title, if D =7, 26, 31, 38 and 61.