Assignment- Number Theory

 

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