DocumentationMathematicaBuilt-in FunctionsMathematical FunctionsNumerical Functions
Further Examples: Mod
Here are a few examples.
When reducing modulo n, you can reduce to any consecutive set of n integers.
You can use Simplify to simplify some expressions involving Mod.
Here an expression equivalent to Mod[m, n] is obtained by using FullSimplify with its ComplexityFunction option.