Primitive Solutions of the Diophantine Euqation x~(d(n))+y~(d(n))=z~(φ(n))

Let n be a positive integer,and let d(n) and φ(n) denote the divisor function and Euler's totient function respectively.Let p be an odd prime.It is proved that if n=1,2,4,or p,then the equation xd(n)+yd(n)=zφ(n) has infinitely many primitive solutions(x,y,z);if n≠1,2,4 p or p2,then the equation has no primitive solution(x,y,z).