A generalized Lucas sequence and permutation binomials

Let p be an odd prime and q = p m . Let l be an odd positive integer. Let p ≡ -1 (mod l) or p ≡ 1 (mod l) and l | m. By employing the integer sequence a n = Σ (2cos π(2t - 1) l) n , which can be considered as a generalized Lucas sequence, we construct all the permutation binomials P(x) = x r + x u of the finite field F q .