Let f be a complex-valued, completely multiplicative,arithmetical function. Assume that there exists an infinite increasing sequence Nk 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 advanced fieldsadvanced fields unsolved