Abstract
We present several existence and nonexistence results for permutation binomials of the form xr(xq−1+a), where e≥2 and a∈Fqe⁎. As a consequence, we obtain a complete characterization of such permutation binomials over Fq2, Fq3, Fq4, Fp5, and Fp6, where p is an odd prime.
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