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## [Axiom-developer] [PrimeField] (new)

**From**: |
Bill Page |

**Subject**: |
[Axiom-developer] [PrimeField] (new) |

**Date**: |
Wed, 12 Jan 2005 16:59:39 -0600 |

http://mathworld.wolfram.com/FiniteField.html
$GF(p)$ is called the prime field of order $p$, and is the field of residue
classes modulo $p$, where the $p$ elements are denoted 0, 1, ..., . $a = b$ in
$GF(p)$ means the same as $a \equiv b\ ({\bf mod}\ p)$. Note, however, that
$2\times 2 \equiv 0\ ({\bf mod}\ 4)$ in the ring of residues modulo 4, so 2 has
no reciprocal, and the ring of residues modulo 4 is distinct from the finite
field with four elements. Finite fields are therefore denoted $GF(p^n)$,
instead of $GF(k)$, where $k=p^n$, for clarity.
http://www.mathematics-online.org/inhalt/aussage/aussage521/
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