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# Finite Field Tables

A field is a set of elements with the four operations of arithmetic satisfying the following properties.  associativity: , ,  commutativity: ,
distributivity: ,
zero and identity: ,  inverses if .
One example of a field is the set of numbers {0,1,2,3,4} modulo 5, and similarly any prime number gives a field, GF(). A Galois field is a finite field with order a prime power ; these are the only finite fields, and can be represented by polynomials with coefficients in GF() reduced modulo some polynomial.
In this Demonstration, pick a prime and polynomial, and the corresponding addition and multiplication tables within that finite field will be shown. Squares colored by grayscale represent the fiield elements.

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