On The Diophantine Equation (35n)~x+(612n)~y=(613n)~z

Indefinite equation is a very important topie in number theory,however,solving the.index of indefinite equation ax+by=czis difficult.In 1956,Jesmabowiez con-jectured that the Diophantine equation (an)x+(bn)y=(cn)z has only the integer solution x=y=z=2,:where a,b,c,are relatively prime numbers each other.In this paper.using the elementary method shows thst:for any positive integer n,indefinite equation(35n)x+(612n)y=(613n)z has only the positive solution x=y =z=2 That is the conjecture of Jesmanowiez holds when a=35,b=612,c=613...