Kátai, I. A remark on additive arithmetical functions. (English) Zbl 0159.05802 Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Math. 10, 81-83 (1967). Generalizing two results of P. Erdős [Ann. Math. (2) 47, 1–20 (1946; Zbl 0061.07902)] the author proves that if \(\varepsilon(n)\) is an arbitrary sequence tending to zero, and \(f(n)\) is additive such that \((f(n+1)-f(n))\geq -\varepsilon(n)\) then \(f(n)=c\log n\). The author notes that this result was stated without proof by P. Erdős [Rend. Sem. Mat. Fis. Milano 27, 45–49 (1958; Zbl 0081.04205)]. Reviewer: W. Narkiewicz Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 6 Documents MSC: 11N64 Other results on the distribution of values or the characterization of arithmetic functions Keywords:additive arithmetic functions PDF BibTeX XML Cite \textit{I. Kátai}, Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Math. 10, 81--83 (1967; Zbl 0159.05802) OpenURL