丢番图方程x^3±1=2pDy^2的整数解

On Integer Solution of the Diophantine Equation x^3±1=2pDy^2

设D=∏r+i(n∈Z),ri≡5 mod 6(1≤i≤n)为彼此不相同的奇素数,p≡1 mod 6为奇素数,关于丢番i=1图方程x3±1=2pDy2的初等解法至今仍未解决.运用Pell方程的解的性质、同余式、平方剩余、递归序列等讨论了丢番图方程x3±1=2pDy2的整数解的情况.

Let D = ∏r＋i（n∈Z）, ri = 5 mod 6 （ 1≤i ≤ n） be different odd primes and p ≡ 1 mod 6 be odd prime. The primary solution of the Diophantine equation x3 ± 1 = 2pDy2 still was unresolved. The integer solutions of the Diophantine equation x3 ± 1 = 2pDy2 were discussed with the help of some proper- ties of the solutions to Pell equation, congruence, quadratic remainder and recursive sequence.