# Number Theory

275

Author: Dr. C. Muthulakshmi @ Sasikala, Dr. R. Ponraj

ISBN: 9789391549398

Copy Right Year: 2023

Pages: 286

Binding: Soft Cover

Publisher: Yes Dee Publishing

Out of stock

SKU: YD9789391549398 Category:

## Description

This book on Number Theory emphasises on the elementary topics including Binomial Theorem, Division Algorithm, Prime Numbers, Congruences and Some special congruences. Features: Many worked examples. Perfect tool for preparing for undergraduate exams. Suitable for independent study. Ideal aid for other fields such as Cryptography, Software Engineering, specifically security-based software.

Weight .3 kg 22 × 14 × 1 cm

## Table of Content

Chapter 1 Number System

1.1 Introduction

1.2 Peano’s Axioms

1.3 Well Ordering Property (WOP) of Positive Integers

1.4 Triangular Numbers

1.5 Pentagonal Numbers

1.6 Catalan Numbers

1.7 Problems

1.7.1 First Principle of Finite Induction

1.7.2 Second Principle of Finite Induction

1.7.3 Problems on Binomial Coefficient

Exercises

Chapter 2 Division Algorithm

2.1 Introduction

2.1.1 Division Algorithm

2.1.2 General Version of Division Algorithm

2.2 Greatest Common Divisor

2.3 Least Common Multiple

2.3.1 The Euclidean Algorithm

2.4 The Linear Diophantine Equation

2.5 Problems on Divisibility

2.6 Problems on gcd and lcm

2.7 Problems on Linear Diophantine Equations

Exercises

Chapter 3 Prime and Composite Numbers

3.1 Introduction

3.2 Fundamental Theorem of Arithmetic

3.3 Twin Primes

3.4 Goldbach Conjecture

3.5 The Sieve of Eratosthenes

Exercises

Chapter 4 Congruences

4.1 Modulo System

4.2 Congruence Modulo n and Basic Properties

4.3 Binary and Decimal Representation of Integers

4.4 Polynomial Congruence

4.5 Tests of Divisibility

4.6 Linear Congruences

4.7 Diophantine Equations

4.8 Problems on Binary and Decimal Representations of Integers

4.8.1 Decimal Representation

Exercises

Chapter 5 Some Special Congruences

5.1 Introduction

5.2 Wilson’s Theorem

5.4 Generalisation of Wilson’s Theorem

5.5 Problems on Fermat’s Theorem

5.6 Problems on Wilson’s Theorem

5.7 Some Factorization Methods

5.7.1 Fermat Kraitchik Factorisation Method

5.7.2 Euler’s Factorization Method

Exercises

Bibliography