MathDB

Let

f

be a complex-valued, completely multiplicative,arithmetical function. Assume that there exists an infinite increasing sequence

N_k

of natural numbers such that f(n)\equal{}A_k \not\equal{} 0 \;\textrm{provided}\ \; N_k \leq n \leq N_k\plus{}4 \sqrt{N_k}\ . Prove that

f

is identically

1

. I. Katai

Problem Statement