##  [Modular Arithmetic](/modular-arithmetic) 

  ##  [Modular Arithmetic](https://puremath.quantumdictionary.io/modular-arithmetic-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The system of arithmetic on integers taken with respect to congruence relations modulo a fixed modulus n; integers are partitioned into residue classes and operations are performed on these classes, yielding the ring Z/nZ and the field F_p when n is prime.