Number theory/Introduction

The following topics make a good introduction to number theory:

• Primes
  • Sieve of Eratosthenes
  • Prime factorization
• Composite numbers
• Divisibility
  • Divisors
    • Common divisors
      • Greatest common divisors
    • Counting divisors
  • Multiples
    • Common multiples
      • Least common multiples
• Division Theorem (the Division Algorithm)
• Base numbers
• Diophantine equations
  • Simon's Favorite Factoring Trick
• Modular arithmetic
  • Linear congruence

Introductory Number Theory Resources

Books

• the Art of Problem Solving Introduction to Number Theory by Mathew Crawford (details)
• General Interest
  • Fermat's Enigma by Simon Singh (details)
  • Music of the Primes by Marcus du Sautoy (details)

Classes

• Introduction to Number Theory Course is part of the AoPS Online School. Details

See also

• Intermediate number theory
• Olympiad number theory