Dickson Polynomials of the Second Kind that are Permutations

Abstract

AbstractIt is known that the Dickson polynomial of the second kind permutes the elements of the finite prime field (p odd) when n + 1 = ±2 to each of the moduli and . Based on numerical evidence it has been conjectured that these congruences are necessary for the polynomial to permute . The conjecture is established here by a new method