Finite fields whose members are the sum of a potent and a 5-potent
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| Format: | Preprint |
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2025
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| _version_ | 1866911367926120448 |
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| author | Zhou, Juncheng Danchev, Peter V. Wu, Hongfeng |
| author_facet | Zhou, Juncheng Danchev, Peter V. Wu, Hongfeng |
| contents | 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 \cite{Cohen} 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_16942 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite fields whose members are the sum of a potent and a 5-potent Zhou, Juncheng Danchev, Peter V. Wu, Hongfeng Number Theory Commutative Algebra Rings and Algebras 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 \cite{Cohen} 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. |
| title | Finite fields whose members are the sum of a potent and a 5-potent |
| topic | Number Theory Commutative Algebra Rings and Algebras |
| url | https://arxiv.org/abs/2512.16942 |