关于Diophantine方程x^3-1=Dy^2(D=p,2p)

On the Diophantine Equation x^3-1=Dy^2(D=p,2p)

运用Pell方程px2-3y2=1的最小解、同余式、平方剩余、勒让德符号等初等方法,证明了p是6k+1型的奇素数时,Diophantine方程x3-1=Dy2(D=p,2p)正整数解的情况。

In this paper the author proves that when 6k q-1 p is an odd prime number Diophantine equation xa-1 = Dy^2 （D = p, 2p） is positive integer solution, based on the minimal solution of Pell equation px^2-3y^2=1, congruence, quadratic residues and Legendre symbols.