Number Theory

Contents

• Ntheory Class Reference
  • Sieve
• Ntheory Functions Reference
  • prime()
  • primepi()
  • nextprime()
  • prevprime()
  • primerange()
  • randprime()
  • primorial()
  • cycle_length()
  • composite()
  • compositepi()
  • smoothness()
  • smoothness_p()
  • trailing()
  • multiplicity()
  • perfect_power()
  • pollard_rho()
  • pollard_pm1()
  • factorint()
  • factorrat()
  • primefactors()
  • divisors()
  • proper_divisors()
  • divisor_count()
  • proper_divisor_count()
  • udivisors()
  • udivisor_count()
  • antidivisors()
  • antidivisor_count()
  • totient
  • reduced_totient
  • divisor_sigma
  • udivisor_sigma
  • core()
  • digits()
  • primenu
  • primeomega
  • mersenne_prime_exponent()
  • is_perfect()
  • is_mersenne_prime()
  • abundance()
  • is_abundant()
  • is_deficient()
  • is_amicable()
  • symmetric_residue()
  • crt()
  • crt1()
  • crt2()
  • solve_congruence()
  • binomial_coefficients()
  • binomial_coefficients_list()
  • multinomial_coefficients()
  • multinomial_coefficients_iterator()
  • npartitions()
  • is_euler_pseudoprime()
  • is_square()
  • mr()
  • is_lucas_prp()
  • is_strong_lucas_prp()
  • is_extra_strong_lucas_prp()
  • isprime()
  • is_gaussian_prime()
  • n_order()
  • is_primitive_root()
  • primitive_root()
  • sqrt_mod()
  • sqrt_mod_iter()
  • quadratic_residues()
  • nthroot_mod()
  • is_nthpow_residue()
  • is_quad_residue()
  • legendre_symbol()
  • jacobi_symbol()
  • discrete_log()
  • continued_fraction()
  • continued_fraction_convergents()
  • continued_fraction_iterator()
  • continued_fraction_periodic()
  • continued_fraction_reduce()
  • count_digits()
  • digits()
  • is_palindromic()
  • mobius
  • egyptian_fraction()
  • pi_hex_digits()
  • ECM function
  • Examples
  • QS function
  • Examples