Fundamental perceptions in contemporary number theory /
Kannan, J. (Mathematician),
Fundamental perceptions in contemporary number theory / J. Kannan, Manju Somanath. - 1 online resource. - Computational Mathematics and Analysis Series . - Computational mathematics and analysis series. .
Includes bibliographical references and index.
Chapter 1 Divisibility -- 1.1. Preliminaries -- 1.2. Division Algorithm -- .1.3. GCD, LCM and Euclidean -- 1.4. The Fundamental Theorem of Arithmetic -- Practical Challenges -- Answers to Practical Challenges -- Challenges From CSIR- NET -- Chapter 2Classical Functions of NumberTheory -- 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 -- Practical Challenges -- Answers to Practical Challenges -- Challenges From CSIR- NET -- Chapter 3Theory of Congruences -- chapter.3.1. Basic Properties of -- 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 -- Practical Challenges -- Answers to Practical Challenges -- Challenges From CSIR- NET -- Chapter 4Primitive Roots and Indices -- 4.1. Order of an Integer -- 4.2. Primitive Roots 4.3. Primitive Root Theorem -- 4.4. Theory of Indices -- Practical Challenges -- Answers to Practical Challenges -- Challenges From CSIR- NET -- Chapter 5Quadratic 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 -- Practical Challenges -- Answers to Practical Challenges -- Chapter 6Special Numbers -- 6.1. Perfect Numbers -- 6.2. Mersenne Numbers -- 6.3. Amicable Numbers -- 6.4. Fermat Numbers -- 6.5. Pell Numbers -- Practical Challenges -- Chapter 7Waring'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.
"The current state and future directions of numerous facets of contemporary number theory are examined in this book "Fundamental Perceptions in Contemporary Number Theory" from a unified standpoint. The theoretical foundations of contemporary theories are unveiled as a consequence of simple challenges. Additionally, this book makes an effort to present the contents as simply as possible. It is primarily intended for novice mathematicians who have tried reading other works but have struggled to comprehend them due to complex reasoning"--
9798886978643
2023019292
Number theory.
QA241
512.7
Fundamental perceptions in contemporary number theory / J. Kannan, Manju Somanath. - 1 online resource. - Computational Mathematics and Analysis Series . - Computational mathematics and analysis series. .
Includes bibliographical references and index.
Chapter 1 Divisibility -- 1.1. Preliminaries -- 1.2. Division Algorithm -- .1.3. GCD, LCM and Euclidean -- 1.4. The Fundamental Theorem of Arithmetic -- Practical Challenges -- Answers to Practical Challenges -- Challenges From CSIR- NET -- Chapter 2Classical Functions of NumberTheory -- 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 -- Practical Challenges -- Answers to Practical Challenges -- Challenges From CSIR- NET -- Chapter 3Theory of Congruences -- chapter.3.1. Basic Properties of -- 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 -- Practical Challenges -- Answers to Practical Challenges -- Challenges From CSIR- NET -- Chapter 4Primitive Roots and Indices -- 4.1. Order of an Integer -- 4.2. Primitive Roots 4.3. Primitive Root Theorem -- 4.4. Theory of Indices -- Practical Challenges -- Answers to Practical Challenges -- Challenges From CSIR- NET -- Chapter 5Quadratic 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 -- Practical Challenges -- Answers to Practical Challenges -- Chapter 6Special Numbers -- 6.1. Perfect Numbers -- 6.2. Mersenne Numbers -- 6.3. Amicable Numbers -- 6.4. Fermat Numbers -- 6.5. Pell Numbers -- Practical Challenges -- Chapter 7Waring'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.
"The current state and future directions of numerous facets of contemporary number theory are examined in this book "Fundamental Perceptions in Contemporary Number Theory" from a unified standpoint. The theoretical foundations of contemporary theories are unveiled as a consequence of simple challenges. Additionally, this book makes an effort to present the contents as simply as possible. It is primarily intended for novice mathematicians who have tried reading other works but have struggled to comprehend them due to complex reasoning"--
9798886978643
2023019292
Number theory.
QA241
512.7