关于丢番图方程x^3-1=511y^2

On the Diophantine Equation x^3-1=511y^2

利用同余式、平方剩余、Pell方程的解的性质、递归序列证明了丢番图方程x3-1=511y2仅有整数解(x,y)=(1,0)和(8,±1).

Using congruence,quadratic residue,some properties of the solutions to Pell equation and recurrent sequence,we prove that the Diophantine equation x3-1=511 y2 only has integer solutions(x,y)=(1,0)and(8,±1).