Subject Code: MA5L016 Subject Name: Number Theory L-T-P: 3-0-0 Credit:3
Pre-requisite(s): Nil
Congruences: linear and polynomial congruences; prime numbers: counting primes, numbers of special forms, pseudo-primes and primality testing; factorization: factorization algorithms; arithmetic functions: multiplicative and additive functions, Euler's phi function, sum and number of divisors functions, the Mobius function and other important arithmetic functions, Dirichlet products; primitive roots and quadratic residues: primitive roots, index arithmetic, quadratic residues, modular square roots; Diophantine equations: linear Diophantine equations, Pythagorean triples, Fermat's last theorem, Tell's, Bachet's and Catalan's equations, sums of squares; Diophantine approximations: continued fractions, convergent, approximation theorems; quadratic fields: primes and unique factorization.
Text Books:
  1. Koshy, Elementary Number Theory with Applications, Academic Press
  2. Burton D.M.  Elementary Number Theory, McGraw Hill
Reference Books:
  1. Rosen K. H. Elementary Number Theory (and it’s applications, Pearson Addison- Wesley
  2. Niven  I.,  Zuckerman  H.S . and Montgomery, H.L. An Introduction to the Theory of Numbers, Wiley
  3. Chandrasekaran K. An Introduction to Analytic Number Theory, Springer
  4. Hardy  G.H. and Wright  E.M. An introduction to the Theory of Numbers, Oxford University Press