On The Diophantine Equation(45n)~x+(1012n)~y=(1013n)~z And (51n)~x+(140n)~y=(149n)~z

In the study of number theory of indeterminate equation is a very important topic,which solve the index of indefinite equation ax + by = cz is one type of difficult.In 1956,Jesmanowicz conjectured that the Diophantine equation(an)x +(bn)y =(cn)z has only the integer solution x = y = z = 2,which a,b,c is two two coprime positive integers.In this paper,using the elementary method showing that:for any positive integer n,indefinite equation(45n)x +(1012n)y =(1013n)z and(51n)x +(140n)y =(149n)z has only the positive solution x = y = z = 2 That is the conjecture of Jesmanowicz holds when a = 45,b = 1012,c = 1013 or a = 51,b = 140,c= 149.