A proof of a conjecture on permutation trinomials

2024/10/30 by Daniele Bartoli, Bartoli, Daniele, Mohit Pal +3
Engineering · Mathematics · #11G20 #11T06 #12E20 #14Q10 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2410.22692

openalex publication_date 2024/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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)=X^q(p-1)+1 +αX^pq+X^q+p-1, on finite fields \mathbbF_q², q=p^k, from [A. Rai, R. Gupta, \it Further results on a class of permutation trinomials, Cryptogr. Commun. 15 (2023), 811--820].

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