Number theory
Number theory is a part of mathematics. It explains what some types of numbers are, what properties they have, and ways that they can be useful.
Topics in number theory are:
Important theorems in number theory are:
 Chinese remainder theorem
 Fundamental theorem of arithmetic
 Fermat's last theorem
 Fermat's little theorem
Applications
A wellknown application of number theory is encrypted messaging (encryption). Data compression also makes use of the field.
Images

A Lehmer sieve, which is a primitive digital computer once used for finding primes and solving simple Diophantine equations.

Title page of the 1621 edition of Diophantus' Arithmetica, translated into Latin by Claude Gaspard Bachet de Méziriac.

Carl Friedrich Gauss's Disquisitiones Arithmeticae, first edition

Riemann zeta function ζ(s) in the complex plane. The color of a point s gives the value of ζ(s): dark colors denote values close to zero and hue gives the value's argument.