NUMBER THEORY

• PRIME NUMBERS
  
  
  • Introduction
  
  
  • Prime Numbers
  
  


• DIVISIBILITY, GCD, AND PRIME FACTORIZATION
  
  
  • Divisbility in \( \mathbb Z \)
  
  
  • Greatest Common Divisors
  
  
  • Prime Factorization
  
  


• MULTIPLICATIVE FUNCTIONS
  
  
  • \( \tau \) and \( \sigma \)
  
  
  • Euler's \( \phi \) Function
  
  
  • Mu and Mobius Inversion Formula
  
  


• THEORY OF CONGRUENCES
  
  
  • Basic Properties of Congruences
  
  
  • Residue Classes
  
  
  • Linear Congruences
  
  
  • Quadratic Congruences and Reciprocity
  
  


• ADDITIONAL TOPICS
  
  
  • RSA Cryptography
  
  
  • Elliptic Curve Cryptography
  
  
  • Continued Fractions
  
  
  • RiemannZeta Functions
  
  

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