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.

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.

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