Number theory

1. NUMBER THEORY Carl Friedrich Gauss, a great mathematician, once remarked that “ mathematics is the queen of sciences, but number theory is the queen of mathematics”. Number theory is the simplest of all types or branches of mathematics that even those without much mathematical training find it very interesting. Properties of Integers The set of integers (denoted by Z ) Z  {..., -3, -2, -1, 0, 1, 2, 3, ...} plays a significant development of the concept of number. It possessed properties that developed mathematical ideas and expounded salient facts.

2. The theory of numbers is primarily concerned with the properties of the natural numbers 1, 2, 3, ..., also called the counting numbers or positive integers. However, the theory is not confined strictly to the set of natural numbers of the set of integers. It is supposed that the student understands (from earlier math subjects) the following properties which the set of integers obey. 1. Closure Laws For any integers a and b, a + b  Z and a · b  Z. However, Z is not closed with respect to division.