Multiplicative functions with $f(p+q-n_0)=f(p)+f(q)-f(n_0)$

Abstract

Let $n_0$ be 1 or 3. If a multiplicative function $f$ satisfies $f(p+q-n_0)=f(p)+f(q)-f(n_0)$ for all primes $p$ and $q$, then $f$ is the identity function $f(n)=n$ or a constant function $f(n)=1$.

arXiv comment7 pages, a variation of Y.-G. Chen, J.-H. Fang, P. Yuan, and Y. Zheng's paper, On multiplicative functions with $f(p+q+n_0)=f(p)+f(q)+f(n_0)$, J. Number Theory 165 (2016), 270--289