We investigate some equations involving the number of divisors d(n); sum σ(n); Euler's totient function ϕ(n); distinct prime factors ω(n); and all (counted with multiplicity) Ω(n). The first part deals equation f(xy) + f(xz) = f(yz). In second part, as an analogy to x2 y2 z2, we study f(x2) f(y2) f(z2) its generalization higher degrees more terms. use just elementary methods basic facts about a...

We give a representation of the classical theory of multiplicative arithmetic functions (MF)in the ring of symmetric polynomials. The basis of the ring of symmetric polynomials that we use is the isobaric basis, a basis especially sensitive to the combinatorics of partitions of the integers. The representing elements are recursive sequences of Schur polynomials evaluated at subrings of the comp...