Leikhman's Theorem on the Decomposition of Values of Multiplicative Functions

Abstract
This paper investigates a new property of multiplicative arithmetic functions. For an arbitrary multiplicative function f and any natural number n, it is established that there exist divisors δ, ω | n such that f(δ) · f(ω) = f(n). The trivial cases δ = 1, ω = n and δ = n, ω = 1 are also allowed.
Based on a computational experiment for all n ≤ 10^7, a classification of multiplicative functions by the type of dominating decompositions is proposed. Three kinds of functions are distinguished: classical (φ, σ), non-trivial (τ, µ) and power (n^k). The obtained results open a new direction in number theory and may serve as a basis for further research.