On multiplicative functions with mean-value one on the set of shifted primes (Q1614910)

The authors prove that there are at most 4 multiplicative functions \(f:\mathbb{N}\to\mathbb{C}\) with the properties \(| f(n)|=1\) and \[ \lim_{x\to\infty}\frac{1}{\pi(x)}\sum_{p\leq x}f(p+1)=1. \] They conjecture that besides \(f=1\) no such functions exist.