Finite field

Definition
A finite field is a field with only finitely many elements.

Some key facts about finite fields include:


 * The characteristic of a finite field must be a prime number.
 * The size of a finite field must be a prime power. In fact, it must be a power of the prime number that is the characteristic of the field.
 * For any prime power, there is a unique (up to isomorphism) finite field whose size equals that prime power.

Combining the above key facts, we denote, for any prime power $$q$$, the unique finite field of size $$q$$ by the symbols $$\mathbb{F}_q$$ or $$GF(q)$$. (Note that GF stands for Galois field in recognition of Galois's pioneering work in field theory).