Number Theory


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:


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.

Additional information

Weight .3 kg
Dimensions 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


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


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


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


Chapter 5 Some Special Congruences

5.1 Introduction

5.2 Wilson’s Theorem

5.3 Quadratic Congruence

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



About the Author


Dr. C. Muthulakshmi @ Sasikala is Associate Professor and Head, Department of Mathematics at Sri Paramakalyani College, Alwarkurichi. She has more than 25 years of teaching experience. She has published several research papers in various national/international journals. She has conducted and organized various training programmes on Recreational Mathematics and Vedic Mathematics with aid from UGC Minor Research Program.

Dr. R. Ponraj is Assistant Professor, Department of Mathematics at Sri Paramakalyani College, Alwarkurichi. He has 15 years of experience in teaching and research. He has presented papers at national and international conferences and has 170 publications in reputed national/international journals. He has served as referee for more than thirty five national and international journals and was also editor-in-chief for proceedings of the national level conference.


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