## Details of MA3104 (Autumn 2016)

 Level: 3 Type: Theory Credits: 3.0

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

Syllabus
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.

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.

References
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