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

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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 Functions-Mobius Functions, Dirichlet Products

Module-V

Sum of Squares

Continued Fractions-Pell's Equation



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