A monic irreducible polynomial of degree having coefficients in the finite field GF(), where for some prime and positive integer , is called a primitive polynomial if all of its roots are primitive elements of GF(). In the polynomial representation of the finite field, this implies that is a primitive element. There is at least one irreducible polynomial for which is a primitive element. In other words, for a primitive polynomial, the powers of generate every nonzero value in the field.