To give an account of elementary number theory with use of certain algebraic methods and to apply the concepts to problem solving.

After completing this module students should be able to understand and solve a wide range of problems about the integers, and have a better understanding of the properties of prime numbers.

Greatest common divisor, congruences, perfect numbers, the prime number counting function, Chebyshev''s estimates and the Riemann zeta function, Fermat''s theorem, pseudoprimes, Euler''s theorem, order of an element, primitive roots, the number and sum of divisors of an integer, primality tests and Carmichael numbers, groups, rings and fields, algebraic methods in number theory, quadratic residues, Legendre symbols, Gauss'' reciprocity law, squares in finite fields, quadratic number fields.