The degrees of the factors of certain polynomials over finite fields.
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- by W. H. Mills
- Proc. Amer. Math. Soc. 25 (1970), 860-863
- DOI: https://doi.org/10.1090/S0002-9939-1970-0263783-0
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Abstract:
Neal Zierler has discovered that the polynomial ${x^{585}} + x + 1$ over $\operatorname {GF} (2)$ is the product of $13$ irreducible factors of degree $45$ and that the polynomial ${x^{16513}} + x + 1$ over $\operatorname {GF} (2)$ is the product of $337$ irreducible factors of degree $49$. We prove a general theorem that includes these results, as well as some other well known results, as special cases.References
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- Oystein Ore, Contributions to the theory of finite fields, Trans. Amer. Math. Soc. 36 (1934), no. 2, 243–274. MR 1501740, DOI 10.1090/S0002-9947-1934-1501740-7
- Neal Zierler, On the theorem of Gleason and Marsh, Proc. Amer. Math. Soc. 9 (1958), 236–237. MR 94332, DOI 10.1090/S0002-9939-1958-0094332-2
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 25 (1970), 860-863
- MSC: Primary 12.25
- DOI: https://doi.org/10.1090/S0002-9939-1970-0263783-0
- MathSciNet review: 0263783