The Waring's problem over finite fields through generalized Paley graphs

Ricardo A. Podestá, Denis E. Videla

We show that the Waring's number over a finite field ${\mathbb{F}}_q$, denoted $g(k,q)$, when exists, coincides with the diameter of the generalized Paley graph $Γ(k,q)=Cay(\mathbb{F…