Permutation polynomials with exponents in an arithmetic progression
Youngho Park, June Bok Lee · Bulletin of the Australian Mathematical Society · 1998
We examine the permutation properties of the polynomials of the type hk, r, s(x) = xr (1 + xs + … + xsk) over the finite field , of characteristic p. We give sufficient and necessary conditions in terms of k and r for hk, r, l(x) to be a permutation polynomial over , for q = p or p2. We also prove that if hk, r, s(x) is a permutation polynomial over , then (k + 1)s = ±1.