Permutation Binomials over Finite Fields
نویسندگان
چکیده
We prove that if xm + axn permutes the prime field Fp, where m > n > 0 and a ∈ Fp, then gcd(m − n, p − 1) > √ p − 1. Conversely, we prove that if q ≥ 4 and m > n > 0 are fixed and satisfy gcd(m − n, q − 1) > 2q(log log q)/ log q, then there exist permutation binomials over Fq of the form xm + axn if and only if gcd(m,n, q − 1) = 1.
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