Number Theory and Its Applications 1st Edition by Satyabrota Kundu, Supriyo Mazumder ISBN 9781032231433 1032231432

Number Theory and Its Applications 1st Edition by Satyabrota Kundu, Supriyo Mazumder – Ebook PDF Instant Download/Delivery: 9781032231433 ,1032231432
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Product details:

ISBN 10: 1032231432
ISBN 13: 9781032231433
Author: Satyabrota Kundu, Supriyo Mazumder

Number Theory and Its Applications 1st Edition 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 Mobüs μ-function

6.5 Worked out Exercises

6.6 Greatest Integer function

6.8 Worked out Exercises

6.9 Exercises:

7 Euler’s Generalization and ϕ-function

7.1 Introduction

7.2 Euler’s ϕ – function

7.3 Worked out Exercises

7.4 Euler’s Theorem

7.5 Worked out Exercises

7.6 Properties of ϕ – 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

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:

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Tags: Satyabrota Kundu, Supriyo Mazumder, Number Theory, Applications