English

A proof of a conjecture on permutation trinomials

Number Theory 2024-10-31 v1 Algebraic Geometry

Abstract

In this paper we use algebraic curves and other algebraic number theory methods to show the validity of a permutation polynomial conjecture regarding f(X)=Xq(p1)+1+αXpq+Xq+p1f(X)=X^{q(p-1)+1} +\alpha X^{pq}+X^{q+p-1}, on finite fields Fq2,q=pk\mathbb{F}_{q^2}, q=p^k, from [A. Rai, R. Gupta, {\it Further results on a class of permutation trinomials}, Cryptogr. Commun. 15 (2023), 811--820].

Keywords

Cite

@article{arxiv.2410.22692,
  title  = {A proof of a conjecture on permutation trinomials},
  author = {Daniele Bartoli and Mohit Pal and Pantelimon Stanica},
  journal= {arXiv preprint arXiv:2410.22692},
  year   = {2024}
}
R2 v1 2026-06-28T19:40:38.870Z