Congruence |
A congruence is an equation in modular arithmetic, i.e., one in which only the remainders relative to some base, known as the "modulus," are significant. |

Continued Fraction |
A continued fraction is a real number expressed as a nested fraction. Such representations may be particualrly useful in number theory. |

Convergent |
(1) An analysis, convergent means tending towards some definite finite value. (2) In the theory of continued fractions, a convergent is a partial sum of continued fraction terms. |

Diophantine Equation |
A Diophantine equation is an equation for which only integer solutions are allowed. |

Divisor Function |
The divisor function of order *k* is the number theoretic function that gives the sum of *k*th powers of divisors of a given integer. |

Elliptic Curve |
An elliptic curve is curve defined by an irreducible cubic polynomial in two variables. |

Euclidean Algorithm |
The Euclidean algorithm is an algorithm for finding the greatest common divisor of two numbers. |

Euler-Mascheroni Constant |
The Euler-Mascheroni constant is the mathematical constant defined as the limit of the difference between the *n*th partial sum of the harmonic series and the natural logarithm of *n* which has value of approximately 0.577. |

Fermat's Last Theorem |
Fermat's last theorem is a famous problem in mathematics conjectured by Pierre Fermat around 1637 but not proved until 1995 which states that any number that is a power greater than two cannot be the sum of two like powers. |

Number Theory |
A field of mathematics sometimes called "higher arithmetic" consisting of the study of the properties of integers. Primes and prime factorization are especially important concepts in number theory. |

Partition |
In number theory, a partition is a way of writing a whole number as a sum of positive integers in which the order of the addends is not significant. |

Perfect Number |
A perfect number is a positive integer that equals the sum of its divisors. |

Prime Counting Function |
The prime counting function is a function that gives the number of primes less than or equal to a given positive number. |

Prime Factorization Algorithms |
Prime factorization algorithms are algorithms that have been devised for determining the prime factors of a given number (a process called prime factorization). |

Prime Number Theorem |
The prime number theorem is a theorem in number theory that specifies the asymptotic frequency of prime numbers. |

Quadratic Reciprocity Theorem |
The quadratic reciprocity theorem is a theorem that tells whether a quadratic equation modulo a prime has a solution. |

Riemann Zeta Function |
The Riemann zeta function is a special function of mathematics and physics that is intimately related to deep results surrounding the prime number theorem. |

Squarefree |
A positive integer is squarefree if it is not divisible by any perfect square greater than one. |

Totient Function |
The totient function is a function that gives the number of positive integers less than or equal to a given number that are relatively prime to it. |

Transcendental Number |
A transcendental number is a number that is not the root of any polynomial with integer coefficients. The opposite of algebraic number. |