Factorization tables for $x^{n}1$ over $\textrm {GF} (q)$
Authors:
Jacob T. B. Beard and Karen I. West
Journal:
Math. Comp. 28 (1974), 11671168
MSC:
Primary 12C05
DOI:
https://doi.org/10.1090/S00255718197403641965
MathSciNet review:
0364196
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Abstract  References  Similar Articles  Additional Information
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 $\Phi ({x^n}  1) < {10^8}$. \[ \begin {array}{*{20}{c}} {q = 2;d = 32} \hfill & {q = 3;d = 27} \hfill & {q = 11;d = 15} \hfill \\ {q = {2^2};d = 16} \hfill & {q = {3^2};d = 15} \hfill & {q = 13;d = 15} \hfill \\ {q = {2^3};d = 16} \hfill & {q = 5;d = 25,n \ne {{23}^\dagger }} \hfill & {q = 17;d = 15} \hfill \\ {q = {2^4};d = 16} \hfill & {q = {5^2};d = 10} \hfill & {q = 19;d = 12} \hfill \\ {q = {2^5};d = 12} \hfill & {q = 7;d = 15} \hfill & {q = 23;d = 10} \hfill \\ \end {array} \]

J. T. B. BEARD, JR., "Computing in ${\text {GF}}(q)$," Math. Comp., this issue.
 Jacob T. B. Beard Jr. and Karen I. West, Some primitive polynomials of the third kind, Math. Comp. 28 (1974). MR 366879, DOI https://doi.org/10.1090/S0025571819740366879X
 Oystein Ore, Contributions to the theory of finite fields, Trans. Amer. Math. Soc. 36 (1934), no. 2, 243β274. MR 1501740, DOI https://doi.org/10.1090/S00029947193415017407
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Additional Information
Keywords:
Factorization,
Galois field,
Euler <IMG WIDTH="20" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\Phi$">function
Article copyright:
© Copyright 1974
American Mathematical Society