# Wolfram Language & System 10.4 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# Modulus

Modulusn
is an option that can be given in certain algebraic functions to specify that integers should be treated modulo n.

## DetailsDetails

• Modulus appears as an option in Solve, Reduce, Factor, PolynomialGCD, and PolynomialLCM, as well as in linear algebra functions such as Inverse, LinearSolve, and Det.
• Arithmetic is usually done over the full ring of integers; setting the option Modulus specifies that arithmetic should instead be done in the finite ring .
• The setting Modulus->0 specifies the full ring of integers.
• Some functions require that Modulus be set to a prime, or a power of a prime. is a finite field when is prime.
• Equations for Modulus can be given in Eliminate and related functions.

## ExamplesExamplesopen allclose all

### Basic Examples  (1)Basic Examples  (1)

Solve equations:

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Factor polynomials:

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Compute inverse:

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