##  [Multiplicative Order Modulo N](/index.php/multiplicative-order-modulo-n) 

  ##  [Multiplicative Order Modulo N](https://puremath.quantumdictionary.io/multiplicative-order-modulo-n-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

For an integer a coprime to N, the multiplicative order is the smallest positive integer k such that a^k ≡ 1 (mod N); it is the order of a in the group (Z/NZ)^×.