Number Theory NNMXY10QRM

URI	`m2://res/NNMXY10QRM`
Kind	course
Creators	Anupam Saikia (instructor)
Scope	in
Ids	course 0022nd079:111103020

Expressions

e1: edition

Language	en

m1: page, IIT Guwahati (record). nptel 111103020

Contents

part 1: Divisibility and Primes
session 1: Introduction
session 2: Decimal Expansion of a Positive Integer
session 3: Euclid's Algorithm
session 4: Coprime Integers
session 5: Prime Numbers
session 6: Prime Number Theorem
session 7: Exercise-1
part 2: Congruence
session 8: Congruence
session 9: Linear Congruence
session 10: Simultaneous Linear Congruences
session 11: System of Congruences with Non-coprime Moduli
session 12: Linear Congruences Modulo Prime Powers
session 13: Fermat's Little Theorem
session 14: Pseudo-primes
session 15: Exercise-2
part 3: Number Theoretic Functions
session 16: Greatest Integer Function
session 17: Euler's function
session 18: RSA Cryptosystem
session 19: Arithmetic Functions
session 20: Mobius Function
session 21: Dirichlet Product
session 22: Exercise-3
part 4: Primitive Roots
session 23: Units Modulo an Integer
session 24: Existence of Primitive Roots for Primes
session 25: Primitive Roots for Powers of 2
session 26: Exercise-4
part 5: Quadratic Residues
session 27: Definition and Examples
session 28: Gauss Lemma
session 29: Quadratic Reciprocity
session 30: Quadratic Residues of Powers of an Odd Prime
session 31: The Jacobi Symbol
session 32: Exercise-5
part 6: Binary Quadratic Forms
session 33: Definition and Examples .
session 34: Discriminant of a Quadratic Form
session 35: Proper Representation and Equivalent Forms
session 36: Uniqueness of Equivalent Reduced Form
session 37: Class Number
session 38: Exercise-6
part 7: Integers of Special Form
session 39: Fermat Primes
session 40: Primes Expressible as a Sum of Two Squares
session 41: Sum of Three Squares
session 42: Exercise-7
part 8: Continued Fractions
session 43: Finite Continued Fractions
session 44: Euler's Rule
session 45: Infinite Continued Fractions
session 46: Periodic Continued Fractions
session 47: Conjugate of a Quadratic Irrational
session 48: Continued Fractions of Reduced Quadratic Irrationals
session 49: Best Rational Approximation to an Irrational
session 50: Pell's Equation
session 51: Exercise-8
part 9: Riemann Zeta Function
session 52: Riemann Zeta Function
session 53: Dirichlet Series
session 54: Exercise -9
part 10: Additional Topics
session 55: Lucas Test for Primality
session 56: Pollard's Method for Factorization
session 57: Fermat's Factorization
session 58: Fermat's Conjecture
session 59: Bibliography
session 60: Index

Catalogue records

nptel: 111103020 (manifestation)