A class of permutation trinomials over finite fields (Q2872667)

Let \(\mathbb F_q\) denote the finite field with \(q\) elements. Binomial permutation polynomials over \(\mathbb F_q\) have been extensively studied. Here the author considers trinomials of the form \(x^{2q-1}+tx^q-x\in\mathbb F_q[x]\). He gives necessary and sufficient conditions on \(q\) and \(t\) to yield a permutation of \(\mathbb F_{q^2}\). The proof is a lengthy computation.