Number Theory and Its Applications
- Length: 356 pages
- Edition: 1
- Language: English
- Publisher: CRC Pr I Llc
- Publication Date: 2022-02-17
- ISBN-10: 1032231432
- ISBN-13: 9781032231433
- Sales Rank: #0 (See Top 100 Books)
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.
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
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