Nonexistence of permutation binomials of certain shapes
Number Theory
2008-06-09 v1
Abstract
Suppose x^m + c*x^n is a permutation polynomial over GF(p), where p>5 is prime, m>n>0, and c is in GF(p)^*. We prove that gcd(m-n,p-1) is not 2 or 4. In the special case that either (p-1)/2 or (p-1)/4 is prime, this was conjectured in a recent paper by Masuda, Panario and Wang.
Keywords
Cite
@article{arxiv.0707.1102,
title = {Nonexistence of permutation binomials of certain shapes},
author = {Ariane M. Masuda and Michael E. Zieve},
journal= {arXiv preprint arXiv:0707.1102},
year = {2008}
}
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6 pages