Factorization tables for 𝑥ⁿ-1 over 𝐺𝐹(𝑞)

Beard, Jacob T. B.; West, Karen I.

doi:10.1090/S0025-5718-1974-0364196-5

Factorization tables for $x\sp{n}-1$ over ${\rm GF}\,(q)$

Authors: Jacob T. B. Beard and Karen I. West
Journal: Math. Comp. 28 (1974), 1167-1168
MSC: Primary 12C05
DOI: https://doi.org/10.1090/S0025-5718-1974-0364196-5
MathSciNet review: 0364196
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Abstract: These tables give the complete factorization of ${x^n} - 1$ over ${\text{GF}}(q),q = {p^a},2 \leqslant n \leqslant d$ as below, together with the Euler $\Phi$ -function of ${x^n} - 1$ whenever $\Phi ({x^n} - 1) < {10^8}$ .

$\begin{displaymath}\begin{array}{*{20}{c}} {q = 2;d = 32} \hfill & {q = 3;d = 27... ... {q = 7;d = 15} \hfill & {q = 23;d = 10} \hfill \\ \end{array} \end{displaymath}$

[1] J. T. B. BEARD, JR., "Computing in ${\text{GF}}(q)$ ," Math. Comp., this issue.
[2] Jacob T. B. Beard Jr. and Karen I. West, Some primitive polynomials of the third kind, Math. Comp. 28 (1974), 1166–1167; addendum, ibid. 28 (1974), no. 128, loose microfiche suppl. C1–C5. MR 0366879, https://doi.org/10.1090/S0025-5718-1974-0366879-X
[3] Oystein Ore, Contributions to the theory of finite fields, Trans. Amer. Math. Soc. 36 (1934), no. 2, 243–274. MR 1501740, https://doi.org/10.1090/S0002-9947-1934-1501740-7