=============
Number Theory
=============

.. module:: sympy.ntheory.generate

Ntheory Class Reference
-----------------------
.. autoclass:: Sieve
   :members:

Ntheory Functions Reference
---------------------------

.. autofunction:: prime

.. autofunction:: primepi

.. autofunction:: nextprime

.. autofunction:: prevprime

.. autofunction:: primerange

.. autofunction:: randprime

.. autofunction:: primorial

.. autofunction:: cycle_length

.. autofunction:: composite

.. autofunction:: compositepi

.. module:: sympy.ntheory.factor_

.. autofunction:: smoothness

.. autofunction:: smoothness_p

.. autofunction:: trailing

.. autofunction:: multiplicity

.. autofunction:: perfect_power

.. autofunction:: pollard_rho

.. autofunction:: pollard_pm1

.. autofunction:: factorint

.. autofunction:: factorrat

.. autofunction:: primefactors

.. autofunction:: divisors

.. autofunction:: proper_divisors

.. autofunction:: divisor_count

.. autofunction:: proper_divisor_count

.. autofunction:: udivisors

.. autofunction:: udivisor_count

.. autofunction:: antidivisors

.. autofunction:: antidivisor_count

.. autoclass:: totient
    :members:

.. autoclass:: reduced_totient
    :members:

.. autoclass:: divisor_sigma
    :members:

.. autoclass:: udivisor_sigma
    :members:

.. autofunction:: core

.. autofunction:: digits

.. autoclass:: primenu
    :members:

.. autoclass:: primeomega
    :members:

.. autofunction:: mersenne_prime_exponent

.. autofunction:: is_perfect

.. autofunction:: is_mersenne_prime

.. autofunction:: abundance

.. autofunction:: is_abundant

.. autofunction:: is_deficient

.. autofunction:: is_amicable

.. module:: sympy.ntheory.modular

.. autofunction:: symmetric_residue

.. autofunction:: crt

.. autofunction:: crt1

.. autofunction:: crt2

.. autofunction:: solve_congruence

.. module:: sympy.ntheory.multinomial

.. autofunction:: binomial_coefficients

.. autofunction:: binomial_coefficients_list

.. autofunction:: multinomial_coefficients

.. autofunction:: multinomial_coefficients_iterator

.. module:: sympy.ntheory.partitions_

.. autofunction:: npartitions

.. module:: sympy.ntheory.primetest

.. autofunction:: is_euler_pseudoprime

.. autofunction:: is_square

.. autofunction:: mr

.. autofunction:: is_lucas_prp

.. autofunction:: is_strong_lucas_prp

.. autofunction:: is_extra_strong_lucas_prp

.. autofunction:: isprime

.. autofunction:: is_gaussian_prime

.. module:: sympy.ntheory.residue_ntheory

.. autofunction:: n_order

.. autofunction:: is_primitive_root

.. autofunction:: primitive_root

.. autofunction:: sqrt_mod

.. autofunction:: sqrt_mod_iter

.. autofunction:: quadratic_residues

.. autofunction:: nthroot_mod

.. autofunction:: is_nthpow_residue

.. autofunction:: is_quad_residue

.. autofunction:: legendre_symbol

.. autofunction:: jacobi_symbol

.. autofunction:: discrete_log

.. automodule:: sympy.ntheory.continued_fraction
   :members:

.. automodule:: sympy.ntheory.digits
   :members:

.. autoclass:: sympy.ntheory.mobius
   :members:

.. module:: sympy.ntheory.egyptian_fraction

.. autofunction:: egyptian_fraction

.. module:: sympy.ntheory.bbp_pi

.. autofunction:: pi_hex_digits