Week 10

Chapters (Discrete Mathematics and Its Applications):

• 4.1 Divisibility and Modular Arithmetic
  • 4.1.1 Introduction
  • 4.1.2 Division
  • 4.1.3 The Division Algorithm
  • 4.1.4 Modular Arithmetic
  • 4.1.5 Arithmetic Modulo m
• 4.3 Primes and Greatest Common Divisors
  • 4.3.1 Introduction
  • 4.3.2 Primes
  • 4.3.6 Greatest Common Divisors and Least Common Multiples
  • 4.3.7 The Euclidean Algorithm
  • 4.3.8 gcds as Linear Combinations
• 4.4 Solving Congruences
  • 4.4.1 Introduction
  • 4.4.2 Linear Congruences
  • 4.4.3 The Chinese Remainder Theorem
  • 4.4.5 Fermat’s Little Theorem

Videos:

• Modular Arithmetic
• Euclidian Algorithm to find the Greatest Common Divisor
• Euclidian Algorithm => Extended Euclidean Algorithm to find inverse of mod
• Extended Euclidean Algorithm => Bezout's identity
• System of Congruences => Chinese Remainder Theorem
• Fermat's Little Theorem
• Intuition of Fermat's Little Theorem
• Fermat–Euler theorem
• Proof of Fermat–Euler Theorem & Fermat's Little Theorem

Exercises:

• TrevTutor: Euclidian Algorithm to find the Greatest Common Divisor