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.
V K Krishnan, formerly, Professor of Mathematics, St. Thomas College, Thrissur, Kerala, obtained his PhD in Mathematics from the University of Calicut, Kerala. He has published many research papers in international journals. His main interest lies in gap Tauberian theorems in summability theory, a branch of classical analysis.
Preface
Basic Properties Of Integers Divisibility Primes The greatest common divisor and least common multiple The binomial coefficients Linear Diophantine equations Congruences Residue systems Linear congruences Lagrange’s Theorem Fermat’s Theorem Pseudoprimes and Carmichael numbers Number-theoretic functions Euler’s function Divisor functions The greatest integer function Quadratic Residues Primitive Roots Miscellaneous Pythagorean triples
Problems Set I Set II Set III Set IV Set V Set VI Set VII Set VIII Set IX Set X
Solutions Set I Set II Set III Set IV Set V Set VI Set VII Set VIII Set IX Set X