# Multiplicative order modulo n

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

[Catalogue presentation and source-binding data](https://ocme.evemisslab.com/data/i18n/catalogue.en.json)



## [Multiplicative order modulo n](https://ocme.evemisslab.com/en/atlas/atlas-multiplicative-order-mod-n/)

For gcd(a,n)=1, the multiplicative order is the smallest positive k with a^k congruent to1 modulo n.

atlas-multiplicative-order-mod-n · canonical_mko

[Multiplicative order modulo n](https://ocme.evemisslab.com/en/mko/mko-multiplicative-order-mod-n/)

## Prerequisite nodes


- [Modular inverse](https://ocme.evemisslab.com/en/atlas/atlas-modular-inverse/)
- [Greatest common divisor and coprimality](https://ocme.evemisslab.com/en/atlas/atlas-gcd-coprime/)
- [Natural-number divisibility](https://ocme.evemisslab.com/en/atlas/atlas-natural-divisibility/)
- [Euler's theorem in number theory](https://ocme.evemisslab.com/en/atlas/atlas-euler-theorem-number-theory/)