A Theorem on Permutations of a Finite Field

Abstract

The purpose of this note is to give a new proof of a theorem of L. Carlitz [ 2 ] and R. McConnel [ 5 ]. The theorem is as follows: THEOREM 1. Let F = GF(p n ) be the finite field of order q = p n and let K — {x ∈ F|x d = 1} for some proper divisor d of q — 1 .