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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The degrees of the factors of certain polynomials over finite fields.


Author: W. H. Mills
Journal: Proc. Amer. Math. Soc. 25 (1970), 860-863
MSC: Primary 12.25
MathSciNet review: 0263783
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0263783-0
Keywords: Factors of polynomials, polynomials over finite fields
Article copyright: © Copyright 1970 American Mathematical Society