---
tag: 02RRHJ7R98
kind: concept
name: Multiplicative order
msc: [11A07]
sources:
  - url: https://en.wikipedia.org/wiki/Multiplicative_order
    locator: lead section
same_as:
  wikidata: Q282723
  wikipedia: Multiplicative order
---

## Summary

The multiplicative order of an integer $a$ modulo $n$, with $a$ coprime to $n$, is the smallest positive exponent $k$ such that $a^k \equiv 1 \pmod n$.
The [[definition of the multiplicative order|0SBRX5CZ5R]] gives the precise form.