Number theory/Introduction

From AoPSWiki

Number theory is the study of integers and an introductory study of number theory involves exploring many common relationships between integers.

Introductory Topics in Number Theory

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