On the indefinite equation x~3-1=py~2

Let D be an odd prime of the form 6k+1.By using the elementary method of the smallest solution of the Pell equation Dx2-3y2=1,congruent formula,quadratic residue,and the nature of legendre sign,this paper obtains the sufficient conditions that Diophantine equation x3-1=py2(P=D,2D,3D) has no integer solution,where D=3n(n+1)+1(n∈N).