Number Theory

Code: MA726 | L-T-P-C: 4-0-0-8

MA726 Number Theory L-T-P-C [4-0-0-8]

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 and Waring's problem; Diophantine approximations: continued fractions, convergent, approximation theorems; quadratic fields: primes and unique factorization.

References:

1. Kenneth H. Rosen, J.G. Michaels, J.L. Gross, J.W. Grossman, D.R. Shier, Handbook of Discrete and Combinatorial Mathematics, CRC Press, 1999
2. I. Niven, H.S. Zuckerman, H.L. Montgomery, An Introduction to the Theory of Numbers, Wiley, 1991.
3. K. Chandrasekaran, An Introduction to Analytic Number Theory, Springer, 1968.