Additive uniqueness sets of arithmetic functions (Q1198938)

The author shows that the only multiplicative arithmetic function \(f(n)\) which is not identically zero on primes and satisfies the functional equation \(f(p)+f(q)=f(p+q)\) for all primes \(p\) and \(q\) is the identity function \(f(n)=n\). The key ingredient in the proof is the well-known result that almost every even integer is a sum of two primes.