This is documentation for Mathematica 9, which was
based on an earlier version of the Wolfram Language.
MATHEMATICA GUIDE

# 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.

## Learning ResourcesLearning Resources

### Tutorials

Related Web Resources

Community

## ReferenceReference

### Factoring & Primes »

FactorInteger find the factors of an integer

PrimeQ test whether an integer is prime

### Congruences & Modular Arithmetic

PowerMod modular powers, roots and inverses

### Diophantine & Other Equations »

Reduce find general solutions to Diophantine equations

FindInstance search for particular solutions to Diophantine equations

Element test field, ring, etc. memberships

### Analytic Number Theory »

DirichletL Dirichlet L-functions

### Additive Number Theory »

IntegerPartitions restricted and unrestricted partitions of integers

PowersRepresentations representations of integers as sums of powers

### Algebraic Number Theory »

ToNumberField operate in a given algebraic number field