Number Theory is a branch of mathematics that deals with the study of integers and the study of properties of those integers. Number theory has many applications to computer science in the form of algorithms, cryptography, and network security.
Number theory originated in antiquity and early Greek philosophy. Greek mathematicians such as Pythagoras and Euclid wrote extensively on the subject. The history of number theory shows a strong influence from Greek mathematics, with algebra being developed from symmetric problems in number theory.
The main focus of number theory is on the properties of the natural numbers. This includes the divisibility, prime numbers, factorization, and the distribution of prime numbers. The study of these properties has helped to form the basis for many new algorithms and techniques used in computer science.
One of the most interesting areas of number theory is cryptography. Cryptographers use number theory to design algorithms to encrypt and decrypt messages. Number theory has also been used in network security protocols such as Diffie-Hellman key exchange and RSA encryption.
Number theory has been useful in many other areas of computer science too. Modern database systems use algorithms based on number theory in order to quickly search for data. Algorithms that are used in computer communications such as digital signature schemes and error-correcting codes use prime numbers and divisibility to send and receive data securely and efficiently.
In general, number theory is an essential building block of computation. Its applications to secure communication, fast algorithms, and cryptography ensure that it will remain important for as long as computers are a part of our lives.
