Modular Order

An element \(x\in \mathbb{Z}_p^*\) is of order \(n\) (denoted \(\abs{x} = n\) if \(n\) is the smallest integer greater than zero such that \(x^n = 1\).

It can be shown that if \(\abs{x} = p - 1\) then \(x\) is a generator on \(\mathbb{Z}_p^*\).