University Question Papers CST 292 Number Theory


Number Theory CST 292 Question Paper  June 2023

Number Theory CST 292 Question Paper June 2022

Number Theory CST 292 Question Paper  July 2021

Comments

Post a Comment

Popular posts from this blog

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...
Read more

Well Ordering Principle

In mathematics, the well-ordering principle states that every non-empty set of positive integers contains a least element. In other words, the set of positive integers is well-ordered by its "natural" or "magnitude" order in which $x$ precedes $y$ if and only if  $y$ is either $x$ or the sum of $x$ and some positive integer (other orderings include the ordering $2,4,6$; and $1,3,5$). The phrase "well-ordering principle" is sometimes taken to be synonymous with the "well-ordering theorem". On other occasions it is understood to be the proposition that the set of integers $\{…,−2,−1,0,1,2,3,…\}$ contains a well-ordered subset, called the natural numbers, in which every nonempty subset contains a least element. Well-ordering Principle: If $S$ is a non-empty set of non-negative integers, then $S$ has a least element, i.e., there is an integer $c \in S$ such that $c \le x$ for all $ x \in S$. The principle of mathematical induction follows direct...
Read more

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 ...
Read more