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Journal Article

# Factorization Tables for $x^n - 1$ Over $\mathrm{GF}(q)$

Jacob T. B. Beard, Jr. and Karen I. West
Mathematics of Computation
Vol. 28, No. 128 (Oct., 1974), pp. 1167-1168
DOI: 10.2307/2005376
Stable URL: http://www.jstor.org/stable/2005376
Page Count: 18

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Topics: Factorization, Polynomials

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## Abstract

These tables give the complete factorization of $x^n - 1$ over $\mathrm{GF}(q), q = p^a, 2 \leqslant n \leqslant d$ as below, together with the Euler $\Phi$-function of $x^n - 1$ whenever $\Phi(x^n - 1) < 10^8$. \begin{align*} q &= 2; d = 32\quad q &= 3; d = 27\qquad q &= 11; d = 15\\ q &= 2^2; d = 16\quad q &= 3^2; d = 15\qquad q = 13; d = 15\\ q &= 2^3; d = 16\quad q &= 5; d = 25, n \neq 23^\dagger\qquad q = 17; d = 15\\ q &= 2^4; d = 16\quad q &= 5^2; d = 10\qquad q &= 19; d = 12\\ q &= 2^5; d = 12\quad q &= 7; d = 15\qquad q &= 23; d = 10\end{align*}

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