# A Generalized Lucas Sequence and Permutation Binomials

@inproceedings{Akbary2006AGL, title={A Generalized Lucas Sequence and Permutation Binomials}, author={Amir Akbary and Qiang Wang}, year={2006} }

- Published 2006

Let p be an odd prime and q = pm. 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 an = l−1 2 ∑ t=1 ( 2 cos π(2t− 1) l )n , which can be considered as a generalized Lucas sequence, we construct all the permutation binomials P (x) = xr + xu of the finite field Fq .

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