标题： 有限域，其元素是强力数与4-强力数的和 显示英文标题

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

摘要： 我们对那些有限域$\mathbb{F}_q$进行分类，其中$q$是某个固定素数的幂，其成员是$n$次幂元素与$n>1$以及 4 次幂元素之和。 显示存在恰好十个非平凡对$(q,n)$在这种情况下成立。 这延续了 Cohen-Danchev 等人最近在 Turk. J. Math. (2024) 中发表的出版物，在其中深入研究了三幂元版本，同时也扩展了 Abyzov-Tapkin 在 Sib. Math. J. (2024) 中建立的该领域最近的结果。 显示英文摘要

摘要： We classify those finite fields $\mathbb{F}_q$, 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).