# All you need to know about number theory

- by Eng. Salem Ala' Al Warawreh
- Last updated: 2022-02-25 12:28:15
- Estimated time to read: 5 minutes

## Number Theory definition

Number theory: is a branch of mathematics that helps to study the set of positive whole numbers and it focuses on the study of the relationships between different sorts of numbers like odd or even, prime or composite numbers.

## Introduction to Number Theory

In number theory, we deal with whole numbers, and to study them we put a rule that a set of numbers follow to classify them like :

• *Odd Numbers*

Numbers that can be written on the form [ 2 * n + 1 , for all n where n >= 0 , n is an integer ]

Example :

1 can be written as ( 2 * 0 + 1 ) so it is an odd number

15 can be written as ( 2 * 7 + 1 ) so it is an odd number

99 can be written as ( 2 * 49 + 1 ) so it is an odd number

•* Even Numbers*

Numbers that can be written on the form [ 2 * n , for all n where n >= 0 , n is an integer ]

Example :

0 can be written as ( 2 * 0 ) so it is an even number

16 can be written as ( 2 * 8 ) so it is an even number

100 can be written as ( 2 * 50 ) so it is an even number

* • Square Numbers*

Numbers that can be written on the form [ n * n , for all n where n >= 0 , n is an integer ]

Example :

1 can be written as ( 1 * 1 ) so it is a square number

16 can be written as ( 4 * 4 ) so it is a square number

100 can be written as ( 10 * 10 ) so it is a square number

* • Cube Numbers*

Numbers that can be written on the form [ n * n * n , for all n where n >= 0 , n is an integer ]

Example :

27 can be written as ( 3 * 3 * 3 ) so it is a cube number

64 can be written as ( 4 * 4 * 4 ) so it is a cube number

125 can be written as ( 5 * 5 * 5 ) so it is a cube number

* • Prime Numbers*

Numbers that can only be divided by 1 and themselves

Example :

17 can only divided by using 1 and 17

17 / 1 = 17

17 / 17 = 1

17 / 2 = 8.5 (NOT A WHOLE NUMBER)

2 can only divided by using 1 and 2

2 / 1 = 2

2 / 2= 1

2 / 3 = 0.6667 (NOT A WHOLE NUMBER)

* • Composite Numbers*

Numbers that can be divided by numbers other than 1 and themselves

Example :

16 can be divided by using 1 and 16 and other numbers

16 / 1 = 16

16 / 2 = 8

16 / 16 =1

9 can be divided by using 1 and 9 and other numbers

9 / 1 = 9

9 / 9 = 1

9 / 3 = 3

## Applications of Number Theory

Number theory has many applications throw our life, prime numbers are used heavily in cryptography and device authentication.

Even data analysis depends on number theory to find some relation that most of the data follow.

Number theory is also used in wireless communication and random number generators.