A characterization of the identity function with equation f(p+q+r)=f(p)+f(q)+f(r)

Abstract

Let f(n) be a multiplicative function such that there exists a prime p 0 at which f does not vanish. In this paper, we prove that if f satisfies the equation f(p+q+r)=f(p)+f(q)+f(r) for all primes p, q and r, then f(n)=n for all integers n≥1.

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Correspondence to Jin-Hui Fang.

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Supported by the National Natural Science Foundation of China, Grant No. 11071121 and Natural Science Foundation of the Jiangsu Higher Education Institutions, Grant No. 11KJB110006.

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Fang, JH. A characterization of the identity function with equation f(p+q+r)=f(p)+f(q)+f(r). Combinatorica 31, 697–701 (2011). https://doi.org/10.1007/s00493-011-2739-8

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Mathematics Subject Classification (2000)

  • 11A25