This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.
 Number Theory Packing a large number of sophisticated algorithms—many recent and original—into a powerful collection of functions, Mathematica draws on almost every major result in number theory. A key tool for two decades in the advance of the field, Mathematica's symbolic architecture and web of highly efficient algorithms make it a unique platform for number theoretic experiment, discovery and proof. FactorInteger — find the factors of an integer PrimeQ — test whether an integer is prime      PowerMod — modular powers, roots and inverses      Reduce — find general solutions to Diophantine equations FindInstance — search for particular solutions to Diophantine equations      Element — test field, ring, etc. memberships      Root — represent an algebraic number RootReduce — reduce algebraic numbers to canonical form GaussianIntegers — allow factorization over Gaussian integers      Rationalize — find rational approximations LatticeReduce — find short bases in integer lattices           IntegerPartitions — find restricted and unrestricted partitions of integers PowersRepresentations — find representations of integers as sums of powers      ToNumberField — operate in a given algebraic number field TUTORIALS Integer and Number Theoretic Functions MORE ABOUT Number Theoretic Functions Diophantine Equations Integer Functions Discrete Math Prime Numbers Cryptographic Number Theory Algebraic Numbers Number Recognition New in 6.0: Number Theory & Integer Functions RELATED LINKS Demonstrations related to Number Theory (The Wolfram Demonstrations Project)