Number Theory

Number Theory

• Arithmetic

• Analytic number theory

  • Multiplicative number theory

    • distribution of primes

    • Prime Number Theorem

    • Riemann zeta function

    • Dirichlet's theorem

  • Additive number theory

    • Goldbach's conjecture

    • Waring's problem

Number theory is a branch of pure mathematics that primarily studies the properties of integers, especially prime numbers, and the properties of other number-theoretic objects made out of integers (rational numbers), or defined as generalizations of the integers (algebraic integers).

Integers can be considered per se, or as solutions to equations (Diophantine geometry).

Questions in number theory are often best understood through the study of analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory).

One may also study real numbers in relation to rational numbers, for example, as approximated by the latter (Diophantine approximation).

Number theory is a branch of math concerned with the behavior of integers. It has important applications in cryptography and in the design of randomized algorithms.

Randomization is an important technique for creating fast algorithms for storing and retrieving objects (hash tables), testing whether two objects are the same (two files), and similar.

Number theory is a branch of math concerned with the behavior of integers. It has important applications in cryptography and in the design of randomized algorithms.

Randomization is an important technique for creating fast algorithms for storing and retrieving objects (hash tables), testing whether two objects are the same (two files), and similar.

Much of the underlying theory depends on divisiblity and primality.