Multiplicative Order
Definition
Given nNn \in \mathbb N and aNa \in \mathbb N coprime with nn, the multiplicative order of aa modulo nn is, equivalently:
The order of aa in the group ((Z/n)×,)((\mathbb Z / n)^\times, \cdot)
The minimal kNk \in \mathbb N such that ak1 (mod n)a^k \equiv 1\ (\text{mod } n)
Also see
additive order



Referenced by: