关于不定方程x^3±1=1455y^2的一个初等解法

On a Primary Solution of the Indefinite Equation x^3±1=1 455y^2

利用同余理论、递归序列,以及Pell方程解的性质证明了不定方程x3-1=1 455y2有整数解(x,y)=(1,0),(4 366,±7 563);而不定方程x3+1=1 455y2仅有整数解(x,y)=(-1,0).

By using congruence,recursive sequence and some properties of the solutions for Pell equation, the following conclusions are proved that the indefinite equation x3-1=1 455y2 has integer solutions（x, y）=（1,0）,and（4 366,±7 563）,and that the indefinite equation x3＋1=1 455y2 has only one integer solution（x,y）=（-1,0）.