Diophantine方程x^3-1=6Dy^2的整数解

Integer Solutions of Diophantine Equation x^3-1 = 6Dy^2

设D=q∏ri(n∈Z+),q≡1(mod6)为奇素数,ri≡-1(mod6)(i=1,2,…,n)为彼此不i=1相同的奇素数.运用同余式、平方剩余、Pell方程的解的性质、递归序列等讨论了Diophantine方程x3-1=6Dy2的整数解的情况.

Let D = q∏n i = 1ri（ n ∈ Z＋）,q ≡1（ mod6） be odd prime and ri≡- 1（ mod6）（ i = 1,2,…,n） be different odd primes. The integer solutions of the equation in title are discussed with the help of congruence,quadratic remainder,some properties of the solutions to Pell equation and recursive sequence.