中文摘要：

设D=∏ni=1ri（n≥2）,ri≡-1（mod 6）（1≤i≤n）为互异的奇素数,P∏sj=1pj（s≥2）,pj≡1（mod 6）（1≤j≤s）为互异的奇素数,利用Pell方程解的性质、同余式、平方剩余、递归序列等,得到当s=2且（p1/p2）=-1时,方程x3±1=2PDy2仅有平凡解的2个充分条件.

英文摘要：

LetD=∏ni=1ri（n≥2）,ri≡-1（mod 6）（1≤i≤n）be different odd primes, and P∏sj=1pj（s≥2）,pj≡1（mod 6）（1≤j≤s） be different odd primes. Based on some properties of the solutions to Pell equation, congruence, quadratic residue and i＇ecursive sequence, two sufficient conditions of the indefinite equation x3±1=2PDy2 are given when it only has trivial solutions where s = 2 and （p1/p2）=-1.