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cover

Elementary Number Theory

A Collection of Problems with Solutions

V K Krishnan

₹ 1075

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Imprint

Universities Press

Year of Publishing

2012

Number of pages

260

ISBN

9788173717437

Format

Paperback

Language

English

Dimensions

180 x 240 mm

Catalogue(s)

Mathematics

  • the Book
  • the Author(s)
  • Table of Contents

This book gives a brief introduction to elementary number theory and includes a collection of three hundred problems and their solutions. Number theory deals with the properties of integers. The most interesting and important property of integers is that of divisibility and congruence.

This is primarily a problem book aimed at school students preparing for talent tests like the mathematical Olympiads. Most of the problems are chosen from question papers of the regional, national and international mathematical Olympiads and the talent tests conducted by the Association of Mathematics Teachers of India. Some are taken from standard textbooks, and some are new.

Undergraduate students keen to learn elementary number theory through interesting problems will find the book a good resource. The book is suitable for self-study since the proofs of theorems and solutions to problems are given in detail.

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V K Krishnan, formerly, Professor of Mathematics, St. Thomas College, Thrissur, Kerala, obtained his PhD in Mathematics from the University of Calicut, Kerala. He is the author of Textbook of Functional Analysis – A Problem-oriented Approach (Prentice-Hall of India) and Fundamentals of Real Analysis (Pearson Education), and has published many research papers in international journals. His main interest lies in gap Tauberian theorems in summability theory, a branch of classical analysis.

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Preface
Chapter 1. BASIC PROPERTIES OF INTEGERS
  1. Divisibility
    Primes
    The greatest common divisor and least common multiple
    The binomial coefficients
    Linear Diophantine equations
  2. Congruences
    Residue systems
    Linear congruences
    Lagrange’s Theorem
  3. Fermat’s Theorem
    Pseudoprimes and Carmichael numbers
  4. Number-theoretic functions
    Euler’s function
    Divisor functions
    The greatest integer function
  5. Quadratic Residues
  6. Primitive Roots
  7. Miscellaneous
    Pythagorean triples
Chapter 2.  PROBLEMS

Set I
Set II
Set III
Set IV
Set V
Set VI
Set VII
Set VIII
Set IX
Set X

Chapter 3.  SOLUTIONS

Set I
Set II
Set III
Set IV
Set V
Set VI
Set VII
Set VIII
Set IX
Set X

Index
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