Finite fields whose members are the sum of a potent and a 4-potent

2025/03/09 by Cohen, Stephen D., Danchev, Peter V., Silva, Tomás Oliveira e · 1 citation
#11T30 #16D60 #16U60 #Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2503.06600

Abstract

We classify those finite fields \mathbbF_q, for q a power of some fixed prime number, whose members are the sum of an n-potent element with n>1 and a 4-potent element. It is shown that there are precisely ten non-trivial pairs (q,n) for which this is the case. This continues a recent publication by Cohen-Danchev et al. in Turk. J. Math. (2024) in which the tripotent version was examined in-depth as well as it extends recent results of this branch established by Abyzov-Tapkin in Sib. Math. J. (2024).

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

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