Characteristic of a field

The order of a finite field is the number of elements in the field. There exists a finite field F of order q if and only if q is a prime power, i. e. , q=p^m where p is a prime number called the characteristic of F, and m is a positive integer.

If m=1, then F is called a prime field. If m >= 2, then F is called an extension field. For any prime power q, there is essentially only one finite field of order q; informally, this means that any two finite fields of order q are structurally the same except that the labelling used to represent the field elements may be different.

Any two finite fields of order q are isomorphic and denote such a field by Fq.