This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# Modulus

 Modulus->nis an option that can be given in certain algebraic functions to specify that integers should be treated modulo n.
• 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 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.
Solve equations:
Factor polynomials:
Compute inverse:
Solve equations:
 Out[1]=
Factor polynomials:
 Out[2]=
Compute inverse:
 Out[3]=
 Scope   (6)
Compute PolynomialGCD over the integers modulo 2:
Factor a polynomial over the integers modulo 3:
Find a GroebnerBasis over the integers modulo 5:
Reduce equations over the integers modulo 7:
Compute the determinant of a matrix modulo 8:
Find a modulus for which a system of equations has a solution:
Factor a polynomial over a finite field:
Factor a polynomial over a finite Extension of rationals:
New in 1