Integer Solution On The Indeterminate Equation X~3-1=7py~2

Let D =7 p, p be odd prime.The primary solution of the indeterminate equation x~3 -1 =Dy~2 still remains unresolved.In this paper,using congruence,Legendre symbol,some properties of solutions to Pell equation and recurrent sequence,we prove that if p =2 3, 3 1,the indeterminate equation x~3 -1 =7py~2 only has integer solution( x, y) =(1, 0).