NUMBER THEORY:

Number theory is the study of positive numbers. These positive integers are a set of natural numbers. Sometimes we add zero in a set of positive numbers in the number theory then that set is called a set of whole numbers but when we skin the zero then that is called a set of natural numbers. This shows us that it zero is added in natural numbers then they become whole numbers and set of natural numbers become equal to set of whole numbers ( N = W). As N belongs to “natural numbers” and W belongs to “whole numbers”.

Number theory is the concern of numbers and especially with the set of natural numbers and this is further divided into few branches of numbers like odd numbers, even numbers, Fibonacci numbers, perfects, squares, 1(modulo 4), 3(modulo 4), etc.

Let me give you some brief description of all these numbers too.

Odd: a set of numbers do not divisible by 2 like { 1,3,5,7,…}

Example: ½=0.5

Even: set of numbers that are divided by 2 like: { 2,4,6,8,…}

Example : 2/ 2 = 1 , 4/2 = 2…

Square: a set of numbers that makes the square like 1 square is 1, 2 square is 4 then the square of 3 is 9, etc. so likewise it would be {1, 4, 9,…}

1 square = 1

2 square = 4

3 square = 9…

Cube: a set of those numbers which make cube like a cube of 1 is 1 and cube of 2 is 8 etc. so it would be like {1, 8, 27, 64,…}

1 cube is equal to 1

2 cube is equal to 8

3 cube is equal to 27…

Prime: set of numbers other than one which is just divided by one and on its self. { 2, 3, 5, …}

Example: 2 is divided by one and 2 just.

3 is divided by one and 3 just.

5 is divided by one and 5 just.

Composite: a set of numbers other than 1 that are not prime and that are divisible by more than 2 numbers. Like { 4 , 6, 8, 9 , 10 , 12, …}

Example: 4 is divided by one, 2 and 4.

6 is divided by one, 2, 3, 6. …

1(modulo 4): set of those numbers which when divided by 4 gives the remainder 1. Like { 1, 5, 9 , 13 …}

Divide 1 with 4 we will get 1

5 divides by 4 we will get 1…

Similarly for 3(modulo 4) which gives 3 remainders when divided by 4. Like { 3, 7, 11, 15,…}

Perfect: a set of those numbers which gives again that original number when we add all of its divisors. Like : { 6 , 28 , 496,…}

Example: divisors of 6 are 1, 2, 3 now if we add them we will again get 6 like 1+2+3=6…

Fibonacci: a set of all those numbers which gives the next number by adding last two numbers, like { 1, 1, 2, 3, 5, 8, 13, 21, ..}

Example: 1+1=2

1+2=3

5+8=13…

And so on.

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