Abstract
Let \(n\) be a positive integer and \({\mathbb {F}}_q\), a finite field of \(q\) elements such that the product of distinct prime factors of \(n\) divides \(q-1\). Equal-degree factorization (EDF) factors a polynomial whose irreducible factors have the same degree. In this paper, for any \(\alpha \in {\mathbb {F}}_q^*\), we characterize all irreducible factors of \(x^n-\alpha \) over \({\mathbb {F}}_q\) using the equal-degree factorization phenomena of binomials and trinomials over \({\mathbb {F}}_q\) under some conditions on \(n, q\), and \(\alpha \).
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Acknowledgements
The authors are very grateful to the reviewers for their detailed comments and suggestions that improved the presentation and quality of this paper. The second author “Deepak“ is thankful to the University Grants Commission (UGC), New Delhi, India, for a Junior Research Fellowship (JRF) with UGC Ref. No. 1121/(CSIR-UGC).
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Singh, M., Deepak Sehrawat Equal-degree factorization of binomials and trinomials over finite fields. J. Appl. Math. Comput. 70, 1647–1672 (2024). https://doi.org/10.1007/s12190-024-02009-3
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DOI: https://doi.org/10.1007/s12190-024-02009-3