The radical factors of f(x) − f(y) over finite fields
Javier Gomez-Calderon · International Journal of Mathematics and Mathematical Sciences · 1996
Let F denote the finite field of order q For f(x) in F[x], let f*(x, y) denote the substitution polynomial f(x) − f(y). The polynomial f*(x, y) has frequently been used in questions on the values set of f(x) In this paper we consider the irreducible factors of f*(x, y) that are “solvable by radicals” We show that if R(x, y) denotes the product of all the irreducible factors of f*(x, y) that are solvable by radicals, then R(x, y) = g(x) − g(y) and f(x) = G(g(x)) for some polynomials g(x) and G(x) in F[x].