On the Diophantine Equation x3+ 27 = 139y2

By using the elementary method of recurrent sequence, congruent formula and quadratic residue, the authors prove that the diophantine equation x3+27 = 139y2 has only the integer solutions (x,y)= (-3,0),(13, 4). In the process of proving the conclusion,the authors also prove that the diophantine equation x3+1 = 417y2 has only the integer solution (x,y)= (-1,0), and then give all integer solutions of x3+27 = 139y2.