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Number Theory CST 292 KTU IV Semester Honors Course Notes Dr Binu V P 9847390760

About me Syllabus Scheme Teaching Plan Model Question Paper University Question Papers Assignment-1 Module-1  Introduction Well ordering principle Group Ring Fields Group Ring Fields in detail Divisibility Modular Arithmetic GCD- Euclidean Algorithm Bezout's Identity Extended Euclidean Algorithm LCM-Least Common Multiple Linear Diophantine Equations Modular Division Module-II Prime Numbers and Prime-Power Factorisation Fermat and Mersenne Prime Primality Testing and Factorization Miller Rabin Primality Testing Algorithm Fermat  Factorization Congruence Modular Exponentiation Linear Congruences Simultaneous Linear Congruences- Chinese Remainder Theorem Fermat's Little Theorem and Euler's Theorem Wilson's Theorem Module-III Congruence with Prime modulus Congruence with Prime power modulus Pseudoprime and Carmichael Numbers Euler's Totient Function Cryptography The Group of Units - Primitive Roots Module-IV Quadratic Residues-Legendre and Jacobi Symbols Arithmetic Func

Scheme CST 292 Number Theory

 

Assignment- Number Theory

 

Syllabus CST 292 Number Theory

NUMBER THEORY- SYLLABUS Module 1:Divisibility and Modular Arithmetic: Finite Fields – Groups, Rings and Fields. Divisibility - Divisibility and Division Algorithms, Well ordering Principle,Bezout’s Identity. Modular Arithmetic- Properties, Euclid's algorithm for the greatest common divisor, Extended Euclid’s Algorithm, Least Common multiple, Solving Linear Diophantine Equations, Modular Division. Module 2:Primes and Congruences: Prime Numbers-Prime Numbers andprime-powerfactorization, Fermat and Mersenne primes.,Primality testing and factorization. Congruences-Linear congruences, Simultaneous linear congruences, Chinese Remainder Theorem, Fermat’s little theorem, Wilson's theorem. Module 3:Congruences with a Prime-Power Modulus&Euler's Function: Congruences with a Prime-Power Modulus-Arithmetic modulo p, Pseudoprimes and Carmichael numbers, Solving congruences modulo prime powers. Euler's Function-Euler’s Totient function, Applications of Euler’s Totient function, T

University Question Papers CST 292 Number Theory

Number Theory CST 292 Question Paper  July 2024 Number Theory CST 292 Question Paper  June 2023 Number Theory CST 292 Question Paper June 2022 Number Theory CST 292 Question Paper  July 2021

Introduction

Welcome to the fascinating world of number theory! Number theory is a branch of pure mathematics that deals with the properties and relationships of numbers. It's one of the oldest branches of mathematics, dating back to ancient times, and it continues to be a vibrant and active field of research today. At its core, number theory focuses on the study of integers and their properties. Integers are whole numbers, including positive numbers, negative numbers, and zero. Number theorists explore various aspects of these integers, seeking patterns, relationships, and structures within the numerical realm. One of the central themes in number theory is prime numbers. Prime numbers are integers greater than 1 that have no positive divisors other than 1 and themselves. They play a fundamental role in number theory and are often considered the building blocks of the integers. The distribution and properties of prime numbers have intrigued mathematicians for centuries and continue to be a

Teaching Plan CST 292 Number Theory