Finite field

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In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that has a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common examples of finite fields are the integers mod p {\displaystyle p} when p {\displaystyle p} is a prime number. The order of a finite field is its number of elements, which is either a prime number or a prime power. For every prime number p {\displaystyle p} and every positive integer k {\displaystyle k} there are fields of order p k {\displaystyle p^{k}} . All finite fields of a given order are isomorphic...

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