Permutation binomials over finite fields
Number Theory
2013-10-08 v3
Abstract
We prove that if x^m + c*x^n permutes the prime field GF(p), where m>n>0 and c is in GF(p)^*, then gcd(m-n,p-1) > sqrt{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 GF(q) of the form x^m + c*x^n if and only if gcd(m,n,q-1) = 1.
Cite
@article{arxiv.0707.1108,
title = {Permutation binomials over finite fields},
author = {Ariane M. Masuda and Michael E. Zieve},
journal= {arXiv preprint arXiv:0707.1108},
year = {2013}
}
Comments
12 pages; various minor changes