Modern Number Theory

By Author: Pierce Brosnan
Total Articles: 127
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Introduction:

Generally introduction to modern Number theory is defined as particularly for the numbers in mathematics .Introduction to modern number theory deals with the properties of numbers and also the types of the number, there are many types of the numbers such as integer, decimal and the fraction. Based on the methods and types the introduction to modern number theory can be subdivided into many fields. Now we can see the introduction to modern number theory and also the types of the introduction to modern number theory

Types of modern number theory:

There are six types of the modern number theory; these types are classified according to the representation of the number. it will be shown as below,

Analytical Number Theory
Algebraic Number Theory
Combinatorial Number Theory
Computational Number Theory
Geometry of Numbers
Analytical number theory:

In this type of number theory we can learn the Riemann zeta function and also the other similar function we called as the dirichlet series .The Riemann zeta function will be defined with the complex ...
... plane .

Algebraic Number Theory:

In this type of the number theory will be used for the discussing about the integer and the rational number there are some examples of the number theories are class groups, discriminates, Galois Theory, field chorology, class field theory and L-functions.

Combinatorial Number Theory

In this type of the number theory we can study about the types of the number are the binomial coefficients, the Fibonacci numbers, Bernoulli numbers, factorials, perfect squares, and partition numbers.

Computational Number Theory

This kind of number theory is mainly used for the algorithm for the computation.

Geometry of Numbers:

This type number theory will be used for the both Euclidean and the non Euclidean geometric forms.

Example problems on introduction to modern number theory:

Example1:

Some numbers are listed below just tell the types of the numbers -9, 11, 8/9, 5 11/3, 0.9, v17

Solution:

-9 – negative Integer
11-positive integer
8 / 9 - Fraction
5 11/3 –mixed fraction
0.9 is the decimal
v17 - Irrational Number
These are the types of the numbers

Example 2:

If the sum of two consecutive integer is 163 find those numbers ?

Solution:

Plug two consecutive integers as x and x+1.

In the question they are given the sum is 163

So we can add the consecutive numbers those are equal to 163.

x + x + 1 = 163

2x + 1 = 163

Subtraction 1 on both sides so only we have to find the value of x

2x = 162(after subtracting 1)

Dividing 2 on both sides we get the x values

=81

So the one number x=81

Another number both are consecutive so x+1=81+1=82

So the consecutive number is 81 and 82

If we add those number means we get the answer 163.(81+82=163)

This is the one method of introduction to modern number theory .

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