A class of permutation binomials over finite fields

Let q be a prime power and f = tx + x(2q-1), where t is an element of F-q*. It was recently conjectured that f is a permutation polynomial of F-q2 if and only if one of the following holds: (i) t = 1, q 1 (mod 4); (ii) t = 3, q equivalent to +/-1 (mod 12); (iii) t = 3, q equivalent to -1 (mod 6). We confirm this conjecture in the present paper. (C) 2013 Elsevier Inc. All rights reserved.