Finite fields whose members are the sum of a potent and a 5-potent

2025/12/16 by Juncheng Zhou, Danchev, Peter V., Zhou, Juncheng +2
Computer Science · Mathematics · #Coding theory and cryptography #Cryptography and Residue Arithmetic #Finite Group Theory Research

paper · doi:10.48550/arxiv.2512.16942

Abstract

We show that there are only finitely many finite fields whose members are the sum of an n-potent element and a 5-potent element. Combining this with the algorithmic results provided by S.D. Cohen \it et al., we confirm in the affirmative the conjecture in \citeCohen concerning all finite fields satisfying this condition. Furthermore, we obtain several elementary results for General problem, proving that the number of finite fields satisfying general condition is also finite.

Citations

• Finite fields whose members are the sum of a potent and a 4-potent
• Rings and finite fields whose elements are sums or differences of tripotents and potents

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