A class of permutation binomials over finite fields

Let q   be a prime power and f=tx+x2q−1f=tx+x2q−1, where t∈Fq⁎. It was recently conjectured that f   is a permutation polynomial of Fq2Fq2 if and only if one of the following holds: (i) t=1t=1, q≡1(mod4); (ii) t=−3t=−3, q≡±1(mod12); (iii) t=3t=3, q≡−1(mod6). We confirm this conjecture in the present paper.