Table of Contents

Preface

About the Authors

Symbols

1. Divisibility
1.1 Preliminaries
1.2 Division Algorithm
1.3 GCD, LCM and Euclidean Algorithm
1.4 The Fundamental Theorem of Arithmetic

2. Classical Functions of Number Theory
2.1 Arithmetic Functions
2.2 Some Classical Arithmetic Functions
2.2.1 The Mobius Function
2.2.2 The Euler Totient Function
2.2.3 The Sum and Number of Divisors
2.3 Greatest Integer Function

3. Theory of Congruences
3.1 Basic Properties of Congruences
3.2 Divisibility Tests
3.3 Theory of Residues
3.4 Linear Congruences
3.5 Congruences of Higher Degree
3.6 Fermat- Little Theorem and its Applications

4. Primitive Roots and Indices
4.1 Order of an Integer
4.2 Primitive Roots
4.3 Primitive Root Theorem
4.4 Theory of Indices

5. Quadratic Reciprocity
5.1 Quadratic Residues and Non Residues
5.2 Legendre Symbol and its Properties
5.3 Jacobi Symbol and its Properties
5.4 Quadratic Reciprocity Law

6. Special Numbers
6.1 Perfect Numbers
6.2 Mersenne Numbers
6.3 Amicable Numbers
6.4 Fermat Numbers
6.5 Pell Numbers

7. Waring’s Problem
7.1 Sum of Two Squares
7.2 Difference of Two Squares
7.3 Sum of Three Squares
7.4 Sum of Four Squares
7.5 Waring’s Problem

Bibliography

Index

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Author’s ORCID iD

J. Kannan – 0000-0001-6197-2119
Manju Somanath – 0000-0002-0655-3947