Galois Fields = fields of finite order (cardinality).
Notation: GF(q) = Galois field of order q.
Theorem: The integers 
where p is
a prime, form the field GF(p) under modulo p addition and
multiplication.
Definition: Let 
be an element in GF(q).
The
order of is the smallest positive integer m such that
.
Theorem: If 
for some 
,
then 
.
Definition: An element with order (q-1) in GF(q) is
called a primitive element in GF(q).
Every field GF(q) contains at least one primitive element 
.
All nonzero elements in GF(q) can be represented as (q-1)
consecutive powers of a primitive element 
Theorem: The order q of a Galois Field GF(q) must be a power of a prime.