On the Diophantine Equation x~3±1=3pD_1y~2

Using the properties of congruence and factorization method in Number theory,the solutions of Diophantine equation x3±1=3pD1y2,was studied,in which p is an odd prime,p=3(24r+19)(24r+20)+1,r is a positive integer,D1=2α·q,α=0 or 1,q is an odd prime,q≡5(mod 6).We proved that the Diophantine equation has no solution.The result showed that this equations was no solution,and promofed the research of this kind of equations.