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A remark on additive arithmetical functions. (English) Zbl 0159.05802
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

MSC:
11N64 Other results on the distribution of values or the characterization of arithmetic functions
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