On additive functions (Q5893818)

In the paper is proved the following: Theorem. Let f be an additive real- valued number-theoretic function; \(A,B>0\) be integers with \((A,B)=1\). Suppose f is non-decreasing on the set \(\{An+B : n=1,2,...\}\). Then \(f(n)=\alpha \log n\) if \((n,A)=1\), where \(\alpha >0\) is a suitable constant. In the case of \(A=1\) and \(B=0\) this is a classical result of P. Erdös.