Number Theory in Mathematics
Number theory is a branch of mathematics that studies numbers, particularly whole numbers, and their properties and relationships. It explores patterns, structures, and the behaviours of numbers in different situations. Number theory deals with the following key concepts:
- Prime Numbers: Properties, distribution, and applications of prime numbers.
- Divisibility: Rules and relationships of numbers dividing each other.
- Greatest Common Divisor (GCD) and Least Common Multiple (LCM): Finding common factors and multiples.
- Modular Arithmetic: Remainders and “clock arithmetic.”
- Number Patterns: Squares, cubes, and other numerical sequences.
- Congruences: Relationships between numbers in modular systems.
Number System
Basic Concepts
- Divisors
- Multiples
- Prime Numbers
- Greatest Common Divisor (GCD)
- Least Common Multiple (LCM)
- Modular Arithmetic
- Co-Prime Numbers
- Euler’s Totient Function
Advanced Concepts
- Chinese Remainder Theorem
- Wilson’s Theorem
- Diophantine Equations
- Linear Diophantine Equations
- Pell’s Equation
- Bezout’s Identity
- Mobius Function
- Mobius Inversion
Prime Distribution
- Distribution of Primes
- Prime Number Theorem
- Goldbach’s Conjecture
- Patterns in Primes
Miscellaneous Topics of Number Theory
- Catalan Numbers
- Fibonacci Sequence
- Farey Sequences
- Pigeonhole Principle
- Perfect Numbers
- Deficient Numbers
- Abundant Numbers
- Amicable Numbers
- Automorphic Numbers
- Magic Numbers
- Triangular Numbers
- Tetrahedral Number
- Hexagonal Numbers
- Lucas Primes
- Hardy-Ramanujan Numbers
Programs for Number Theory
- Find the GCD of two number
- Find the LCM of two number
- Calculate the Factorial of a number
- Basic and Extended Euclidean algorithms
- Primality Test to check if a number is prime or not
- Primality Test to check if a number is prime or not using Fermat Method
- Primality Test to check if a number is prime or not using Miller–Rabin
- Primality Test to check if a number is prime or not using Solovay-Strassen
Number Thoery Books
- Elementary Number Theory by David M. Burton
- An Introduction to the Theory of Numbers by G.H. Hardy and E.M. Wright
- A Classical Introduction to Modern Number Theory by Kenneth Ireland and Michael Rosen
- Algebraic Number Theory by Jürgen Neukirch
FAQs on Number Theory
What is Number Theory?
Number Theory or Theory of Numbers is a branch of mathematics that deals with positive numbers and its applications.
Who are Credited to have First Developed the Number Theory?
People of Babyloian Civilization are credited to have first developed the concept of Number Theory.
Who are some popular Number Theorists?
Some of the popular Number Theorists include Pythagoras, Euclid, Fermat, Gauss, Aryanhatta, Brahmagupt and Ramanujan.
What are the Branches of Number Theory?
The different Branches of Number Theory are Elementary Number Theory, Algebraic Number Theory, AnalyticaL Number Theory and Dipohantine Number Theory.
What is Pythagorean Triplet?
Pythagorean Triplet is a collection of three numbers such that the square of the largest number is equal to the sum of the squares of the rest two numbers.
What are the different Numbers System in which Numbers can be written?
The different forms in which numbers can be written are Binary System, Decimal System, Octal System and Hexadecimal System.
What is Hardy Ramanujan Number?
1729 is known as Hardy Ramanujan Number as it can be represented as sum of cubes of two different pairs of number. 1729 = 123 + 13 and also 1729 = 103 + 93
Who is the Father of Number Theory?
Pierre de Fermat is regarded as the father of Number Theory.
