Mean Values of Arithmetic Functions under Congruences with the Euler Function.

We consider examining the average order of some arithmetic functions written as sums over divisors d of n satisfying ϕ(d) ≡ a mod p and
f(ϕ(d)) ≡ a mod p such that p is a prime number that is coprime with the
integer a and f is a polynomial function with integer coefficients and a degree
d ≥ 2 that is not constant modulo p.