Some relations among arithmetical functions

Abstract. We consider some possible relations among \(q\)-additive and completely multiplicative functions. We proved that if \(f\) is completely multiplicative and \(q\)-additive function, then either \(f(n)=n\) for every \(n\in{\Bbb N}\) or \(f(n)\) is the Dirichlet character \(\pmod {q_0}\), where \(q_0\vert q\).