On The Diophantine Equation(57N)~x+(1624n)~y=(1625n)~z

Indeterminate equation is a very important topic in number theory,however, solving the index of indefinite equation ax+by=cz is one type of diffcult.In1956the Jesmanowicz conjecture on Diophantine equation(an)x+(bn)y=(cn)z has only the positive integer solution x=y=z-2,which a,b,c is two two coprime positive integers.In this paper,using the elementary methods that:for any positive integern,exponential indefinite equation(57n)x+(1624n)y=(1625n)z has only the positive integer solution x=y=z=2.That is a=57,b=1624,c=1625:whecn the Jesmanowicz conjecture.