On existence of some special pair of primitive elements over finite fields

2020/02/05 by Cícero Carvalho, J. P. G. Sousa, Carvalho, C. +5
Computer Science · Mathematics · #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2002.01867

openalex publication_date 2020/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we generalize the results of Sharma, Awasthi and Gupta (see \citeSAG). We work over a field of any characteristic with q = p^k elements and we give a sufficient condition for the existence of a primitive element α∈ \mathbbF_p^k such that f(α) is also primitive in \mathbbF_p^k, where f(x) ∈ \mathbbF_p^k(x) is a quotient of polynomials with some restrictions. We explicitly determine the values of k for which such a pair exists for p=2,3,5 and 7.

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