Let n be a positive integer.Proved that under some conditions Diophantine equation xd(n)+yϕ(n)=zσ(n)has no positive integer solution(x,y,z),where d(n),ϕ(n)and σ(n)denote the divisor function,Euler totient function and the sum of distinct divisors of n respectively.Additionally,all positive integer solutions of the equation when n=3 are given.
Diophantine equationpositive integer solutiondivisor functionEuler totient functionsum of divi-sor function
NETL
NSTL
万方数据
