Number theory

Number theory is the field of mathematics associated with studying the integers.

Student Guides to Number Theory

• Introductory topics in number theory -- Covers different kinds of integers such as prime numbers, composite numbers, and their relationships (multiples, divisors, and more). Also includes base numbers and modular arithmetic.
• Intermediate topics in number theory
• Olympiad number topics in number theory
• Advanced topics in number theory

Resources

Books

• Introductory
  • 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)

Miscellaneous

• Intermediate
  • Intermediate Number Theory (Details)
• Olympiad
  • Number Theory by Naoki Sato

Other Topics of Interest

These are other topics that aren't particularly important for competitions and problem solving, but are good to know.

• Fermat's Last Theorem

Famous Unsolved Number Theory Problems

• Birch and Swinnerson-Dyer Conjecture
• Collatz Problem
• Goldbach Conjecture
• Riemann Hypothesis
• Twin Prime Conjecture