# A Note on Permutation Binomials and Trinomials over Finite Fields

### New Zealand Journal of Mathematics

Vol. 48, (2018), Pages 25-29

Neranga Fernando

Department of Mathematics,

Northeastern University,

Boston, MA 02115

Abstract Let p be an odd prime and e be a positive integer. We completely explain the permutation binomials and trinomials arising from the reversed Dickson polynomials of the (k + 1)-th kind Dn,k(1,x) over $\mathbb{F}_{p^e}$ when n = pl + 2, where $l\in \mathbb{N}$.

Keywords Finite field, Permutation polynomial, Binomial, Trinomial, Reversed Dickson polynomial.

Classification (MSC2000) 11T06, 11T55.