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
DOI:
https://doi.org/10.1090/S0002-9939-1970-0263783-0
MathSciNet review:
0263783
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Abstract | References | Similar Articles | Additional Information
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.
- Solomon W. Golomb, Shift register sequences, Holden-Day, Inc., San Francisco, Calif.-Cambridge-Amsterdam, 1967. With portions co-authored by Lloyd R. Welch, Richard M. Goldstein, and Alfred W. Hales. MR 0242575
- Oystein Ore, Contributions to the theory of finite fields, Trans. Amer. Math. Soc. 36 (1934), no. 2, 243–274. MR 1501740, DOI https://doi.org/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 https://doi.org/10.1090/S0002-9939-1958-0094332-2
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Keywords:
Factors of polynomials,
polynomials over finite fields
Article copyright:
© Copyright 1970
American Mathematical Society