Modular Arithmetic
Congruence
Properties of Congruence
Modular Addition and Multiplication
forms a ring. It is a field if and only if is prime.
Linear Congruences
Example
Solve :
, so solution exists and is unique mod .
(since )
Fermat's Little Theorem
Wilson's Theorem
Euler's Theorem
Applications
Modular Exponentiation
Example:
, , ,