Table of contents
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.