The primitive element theorem.

Let p be a prime number. Then there exists an integer q such that:
	
	1. 0<q<p;
	2. For any number m relatively prime to p, there exists an integer e such that q^e = m(mod p).

The number q is called a primitive root (element) modulo p. The powers of q generate all the elements
of the multiplicative group of the nonzero elements modulo p. In other words, q^(p-1) = 1 (mod p)
and for any other number d, 0<d<p-1 we can't have q^d = 1(mod p).

Exemple for p=13;

A primitive element mod 13 is 2.
Indeed, the powers of 2 mod 13 are 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1. 2^12 = 1(mod 13) and
2^d !=1 (mod 13) for 0<d<12.
A nonprimitive element mod 13 is 4. That's because 4^6 = 1 (mod 13). The subgrup generated by the 
powers of 4 (mod 13) has the order 6 (not 12, which should be order of any primitive element).