English

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}
}

Comments

6 pages

R2 v1 2026-06-21T08:56:08.085Z