On a conjecture of Fernando, Hou and Lappano concerning permutation polynomials over finite fields

摘要

Let F-q be the finite field with q elements and let p = char F-q. It was conjectured that for integers e = 2 and 1 = a = pe - 2, the polynomial Xq-2 + Xq(2-2) + ... + Xq(a-2) is a permutation polynomial of F-qe if and only if (0 a = 2 and q = 2, or (ii) a = 1 and gcd(q - 2, q(e) - 1) = 1. In the present paper we confirm this conjecture. (C) 2018 Elsevier Inc. All rights reserved.