On the Diophantine Equation x~3+1=57y~2

In this paper the author studies all the integer solutions to the diophantine equation x3+1=57y2.The process is as follows:classify the will-be integer solutions to the diophantine equation into four equations by equation firstly,then take models on these equations,the first equation and second equantion aren't integer solutions.At last two equations are integer solutions,at the same time,the methods of recursive sequences and maple formality and Pell equation and quadratic remainder are used.At last,it is proved that the diophantine equation x3+1=57y2 has only positive integer solutions(x,y)=(-1,0),(8,±3).