Multiplicative functions satisfying a congruence property. V (Q1310432)

[For Part III, cf. Publ. Math. 39, No. 1/2, 149-153 (1991; Zbl 0749.11009).] \textit{M. V. Subbarao} [Can. Math. Bull. 9, 143-146 (1966; Zbl 0151.02803)] proved that a multiplicative function \(f\) satisfying the condition \(f(n+m)\equiv f(m)\bmod n\) for all integers \(n\), \(m\) has the form \(f(n)= n^ c\) where \(c\) is a non-negative integer. There are many generalizations of this result. In the present paper the author determines all multiplicative functions \(f\) such that \(f(An+B) \equiv C\bmod n\) holds for \(n\geq N\). Here \(A>0\), \(B>0\), \(C\neq 0\), \(N>0\) are fixed integers with \((A,B)=1\).