Research Of Several Diophantine Equation About X~3+1=Dy~2

For Diophantine equation x~3+1-Dy~2,this article proves that when D=2×79=158,the Diophantine equation x~3+1=158y~2 have only integer solutions(x,y)=(-1,0),(293,±399);when D=2×463=926,the Diophantine equation x~3+1=926y~2 have only integer solutions(x,y)=(-1,0),(485,±351);when D=2×127=254,the Diophantine equation x~3+1=254y~2 has only integer solution(x,y)=(-1,0);The necessary and sufficient conditions of the Diophantine equation's solution to the x~3+1=2py~2,p?7(mod8)is p=A(12a4-6a2+1)and the solution is(x,y)=(6a2-1,3aA(12a4-6a2+1)).This paper also studies the relationship between the solutions of the Diophantine equation x~3+8=Dy~2 and Diophantine equation x~3+27=Dy~2 with the Diophantine equations x~3+1=Dy~2.