Details of MA3104 (Autumn 2016)

Level: 3 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
MA3104 Elementary Number Theory Shibananda Biswas

MA3104 Elementary Number Theory

Fundamental notions: Mathematical induction, divisibility, greatest common divisor and Euclidean algorithm, prime numbers and unique farctorization.

Arithmetic functions: Multiplicative functions, Mobius function and Mobius inversion, Eulers totient function, greatest integer function, average orders of arithmetic functions.

Congruences: Definition and basic properties, congruence powers and Eulers theorem, linear congruence equations, simultaneous linear equations and Chinese remainder theorem, polynomial congruences, order and primitive roots.

Quadratic residues and the quadratic reciprocity law: Quadratic residues, Legendre symbol, Gauss lemma, Quadratic reciprocity law, Jacobi symbol.

Sums of squares: Pythagorean triplet, representations of integers as sums of two squares and sums of four squares.

Binary quadratic forms: Introduction to binary quadratic forms, equivalence, reduction of binary quadratic forms and class number, representations of numbers by binary quadratic forms.

Continued fractions and Pells equation: Finite and infinite continued fractions, purely periodic continued fractions, Continued fraction expansion of square roots of positive numbers, Pells equation and solutions.

Cryptography: Block and stream ciphers, public key cryptosystems using RSA, El Gamal cryptosystem.

Suggested Texts/Reference Books:

1. Burton, D, M., Elementary Number Theory (6th Edition), Tata McGraw-Hill, 2007.

2. Koshy, T., Elementary Number Theory with Applications (2nd Edition), Academic Press, 2007.

3. Le Veque, W, J., Topics in Number Theory, Volumes I & II, Dover Publications, 2002.

4. Rosen, K, H., Elementary Number Theory and Its Applications (5th Edition), Addison-Wesley, 2000.

Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 1 Core
2 IP 3 Not Allowed
3 IP 5 Not Allowed
4 MR 1 Not Allowed
5 MR 3 Not Allowed
6 MS 5 Core
7 RS 1 Not Allowed
8 RS 2 Not Allowed