For a finite field F of characteristic 2, an integer n≥ 3 , and for a function f: F→ F, if there is a function h: F→ F such that the divided difference f[x<inf>1</inf>, ⋯ , x<inf>n</inf>] on any n distinct elements of F satisfies f[x<inf>1</inf>, … , x<inf>n</inf>] = h(x<inf>1</inf>+ ⋯ + x<inf>n</inf>) , then f is a polynomial of degree at most n over F. This makes earlier work of Davies and Rousseau complete.
