Course Details
Subject {L-T-P / C} : MA3104 : Number Theory { 3-1-0 / 4}
Subject Nature : Theory
Coordinator : Prof. Gopal Krishna Panda
Syllabus
Division Algorithm, Prime and composite numbers, Fibonacci and Lucas Numbers, Fermat numbers, Greatest common divisors, Euclidean algorithm, Fundamental theorem of arithmetic, Linear Diophantine equations, Complete residue systems, Linear Congruences, System of linear congruences, Chinese remainder theorem, Pollard rho factoring methods, Wilson’s theorem, Fermat’s little theorem, Euler’s theorem, Pollard p-1 factoring method, Multiplicative functions, Euler’s phi function, Tau and sigma functions, Perfect numbers, Mersenne primes, Primitive roots and indices, Order of a positive integer, Primality test, Primitive roots of primes, Algebra of indices, Cryptology, Affine ciphers, Hill ciphers, Exponentiation ciphers, The RSA cryptosystem, The Knapsack ciphers.
Course Objectives
- To make the student familiar with modular arithmetic
- To show the power of modular arithmetic in solving difficult problems easily
- To introduce the concepts of different cryptosystems
- To introduce how large primes are discovered and their usefulness in RSA cryptography
Course Outcomes
This course will make the student confident to work with very large numbers. They will realize how number theory is so useful in day-to-day life.
Essential Reading
- G. E. Andrews, Number Theory, Courier Dover Publications , 2012
- Thomas Koshy, Elementary Number Theory with Applications, Elsivier , 2007
Supplementary Reading
- David Burton, Elementary Number Theory, McGraw-Hill , 2002
- G. H. Hardy and E.M. Wright, An Introduction to the Theory of Numbers, Oxford University Press , 2008