Number Theory and its Applications

✍ Scribed by Satyabrota Kundu, Supriyo Mazumder

• Publisher: CRC Press
• Year: 2022
• Tongue: English
• Leaves: 366
• Edition: 1
• Category: Library

✦ Synopsis

Number Theory and its Applications is a textbook for students pursuing mathematics as major in undergraduate and postgraduate courses.

Please note: Taylor & Francis does not sell or distribute the print book in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.

✦ Table of Contents

Cover
Title Page
Dedication
Copyright Page
Preface
Table of Contents
1 Prerequisites
2 Theory of Divisibility
2.1 Introduction
2.2 Divisibility
2.3 Worked out Exercises
2.4 Greatest Common Divisor
2.5 Least Common Multiple
2.6 Worked out Exercises
2.7 Linear Diophantine Equations
2.8 Worked out Exercises
2.9 Exercises:
3 Prime Numbers
3.1 Introduction
3.2 Primes & Fundamental Theorem of Arithmetic
3.3 Worked out Exercises
3.4 Exercises:
4 Theory of Congruences
4.1 Introduction
4.2 Congruences
4.3 Worked out Exercises
4.4 Linear Congruences
4.5 Worked out Exercises
4.6 System of Linear Congruences
4.7 Worked out Exercises
4.8 Exercises:
5 Fermat’s Little Theorem
5.1 Introduction
5.2 Fermat’s Little Theorem
5.3 Worked out Exercises
5.4 Wilson’s Theorem
5.5 Worked out Exercises
5.6 Exercises:
6 Arithmetic Functions
6.1 Introduction
6.2 The Sum and Number of Divisors
6.3 Worked out Exercises
6.4 Mobiüs μ-function
6.5 Worked out Exercises
6.6 Greatest Integer Function
6.7 Worked out Exercises
6.8 Exercises:
7 Euler’s Generalization and Ø–function
7.1 Introduction
7.2 Euler’s Ø–function
7.3 Worked out Exercises
7.4 Euler’s Theorem
7.5 Worked out Exercises
7.6 Properties of Ø–function
7.7 Worked out Exercises
7.8 Exercises:
8 Primitive Roots
8.1 Introduction
8.2 Multiplicative Order
8.3 Worked out Exercises
8.4 Primitive Roots for Primes
8.5 Worked out Exercises
8.6 Existence of Primitive Roots
8.7 Worked out Exercises
8.8 Index Arithmetic
8.9 Worked out Exercises
8.10 Exercises:
9 Theory of Quadratic Residues
9.1 Introduction
9.2 Quadratic Residues and Nonresidues
9.3 Worked out Exercises
9.4 Quadratic Reciprocity Law
9.5 Worked out Exercises
9.6 The Jacobi Symbol
9.7 Worked out Exercises
9.8 Exercises:
10 Integers of Special Forms
10.1 Introduction
10.2 Perfect Numbers
10.3 Worked out Exercises
10.4 Mersenne Primes
10.5 Worked out Exercises
10.6 Fermat Numbers
10.7 Worked out Exercises
10.8 Exercises:
11 Continued Fractions
11.1 Introduction
11.2 Finite Continued Fractions
11.3 Worked out Exercises
11.4 Infinite Continued Fractions
11.5 Worked out Exercises
11.6 Periodic Fractions
11.7 Worked out Exercises
11.8 Exercises:
12 Few Non-Linear Diophantine Equations
12.1 Introduction
12.2 Pythagorean Triples
12.3 Worked out Exercises
12.4 Fermat’s Last Theorem
12.5 Worked out Exercises
12.6 Exercises:
13 Integers as Sums of Squares
13.1 Introduction
13.2 Sum of Two Squares
13.3 Worked out Exercises
13.4 Sum of More than Two Squares
13.5 Worked out Exercises
13.6 Exercises:
14 Certain Applications on Number Theory
14.1 Fibonacci Numbers
14.2 Worked out Exercises
14.3 Pseudo-random Numbers
14.4 Worked out Exercises
14.5 Cryptology
14.6 Worked out Exercises
14.7 Exercises:
Bibliography
Index