Resumen de On f(p)+f(q)=f(p+q) for all odd primes p and q

Kang-Kang Chen, Yong-Gao Chen

• We characterize all nonvanishing multiplicative functions f for which f(p)+f(q) = f(p+q) for all odd primes p, q. As a corollary, a multiplicative function f is the identity function if and only if f(3) = 3 and f(p) + f(q) = f(p + q) for all odd primes p, q.

  Two questions posed by Claudia A. Spiro in 1992 are answered negatively. Two new conjectures are posed.