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# Number Theory

## Category Documents

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euler
Euler numbers and polynomials

factorial
compute factorial

ifactor
integer factorization

ifactors
integer factorization

isolve
solve equations for integer solutions

isprime
primality test

ithprime
determine the ith prime number

nextprime
determine the next largest prime

numtheory/GIgcd
gcd of Gaussian integers

numtheory/bigomega
number of prime divisors counted with multiplicity

numtheory/cfrac
compute a regular or simple continued fraction expansion

numtheory/cfracpol
compute simple continued fraction expansions for all real roots of a rational polynomial

numtheory/cyclotomic
calculate cyclotomic polynomial

numtheory/divisors
the set of positive divisors

numtheory/factorEQ
integer factorization in Z(sqrt(d)) where Z(sqrt(d)) is a Euclidean ring

numtheory/factorset
prime factors of an integer

numtheory/fermat
nth Fermat number

numtheory/imagunit
square root of -1 mod n

numtheory/integral_basis
integral bases of algebraic number fields

numtheory/invcfrac
convert a simple periodical continued fraction expansion to a quadratic surd

numtheory/issqrfree
test if integer is square free

numtheory/jacobi
Jacobi symbol

numtheory/kronecker
Inhomogeneous Diophantine approximation

numtheory/lambda
Carmichael's lambda function

numtheory/legendre
Legendre symbol

numtheory/mcombine
Chinese remaindering

numtheory/mersenne
nth Mersenne prime

numtheory/migcdex
compute solutions to the modulo N extended GCD problem

numtheory/minkowski
solve Minkowski's linear forms (homogeneous diophantine approximation)

numtheory/mipolys
number of monic irreducible univariate polynomials

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