Multiplicative Order -- from Wolfram MathWorld

Let n be a positive number having primitive roots. If g is a primitive root of n, then the numbers 1, g, g^2, ..., g^(phi(n)-1) form a reduced residue system modulo n, where phi(n) is the totient function. In this set, there are phi(phi(n)) primitive roots, and these are the numbers g^c, where c is relatively prime to phi(n). The smallest exponent e for which b^e=1 (mod n), where b and n are given numbers, is called the multiplicative order (or sometimes haupt-exponent or modulo order) of b...