On the equation \(f(n^2+nm+m^2)=f(n)^2+f(n)f(m)+f(m)^2\)

Abstract. We give all solutions of the equation $$ f\bigl(n^2+nm+m^2\bigr)=f(n)^2+f(n)f(m)+f(m)^2, $$ where \(f\) is an arbitrary complex valued function defined on \(\mathbb{N}\).