A certain property of polynomials (Q794705)

This paper is devoted to the study of polynomials f which satisfy an equation \(f(\alpha x+\beta)=f(x)\) where \(\alpha\) and \(\beta\) are given. Suppose that \(f(\alpha x+\beta)=f(x).\) If \(\alpha \neq \pm 1\) and \(\deg f\geq 3,\) then \(f(x)=(x+\beta /(\alpha -1))^ n+C,\) where \(\alpha\) is an nth root of unity, \(\beta\) and C are constants. Two more results are also established.