ABSTRACT
This chapter provides a discussion of some of the ideas and some of the history of number theory as seen through the themes of Diophantine equations, modular arithmetic, the distribution of primes, and cryptography. The part of number theory called Diophantine equations, which studies integer solutions of equations, is named in his honor. For example, the Chinese Remainder Theorem is a fundamental and essential result in modular arithmetic and was discussed by Sun Tzu. In 1966, Jingrun Chen proved that every sufficiently large even integer is either a sum of two primes or the sum of a prime and a number that is the product of two primes. Although the basic purpose of cryptography is to protect communications, its ideas have inspired many related applications. Although most people think of the Elements as a book concerning geometry, a large portion of it is devoted to the theory of numbers.
