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

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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...
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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...
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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...
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