g is a primitive root modulo n if the multiplicative order of g mod n is φ(n). Equivalently, g generates the group (ℤ/nℤ)*. Not every n has a primitive root (e.g. n has one iff n = 1,2,4, p^a, or 2p^a).. The key formula is order of g = φ(n). This concept is typically introduced in College. Understanding this concept builds a strong foundation for more advanced mathematics.