On multiplicative functions with f(p + q + n0)=f(p)+f(q)+f(n0)

TextLet f(n)f(n) be a multiplicative function such that f   does not vanish at some prime p0p0. In this paper, it is proved that, for any given integer n0n0 with 1≤n0≤1061≤n0≤106, if f(p+q+n0)=f(p)+f(q)+f(n0)f(p+q+n0)=f(p)+f(q)+f(n0) for all primes p and q, then f   must be the identity function: f(n)=nf(n)=n for all integers n≥1n≥1. If a variation of Goldbach's conjecture is true, then the result is true for any fixed integer n0n0.VideoFor a video summary of this paper, please visit https://youtu.be/uGtHiVBZGj0.