Number theory

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


Number theory is a broad topic, and may cover many diverse subtopics, such as:

Some branches of number theory may only deal with a certain subset of the real numbers, such as integers, positive numbers, natural numbers, rational numbers, etc. Some algebraic topics such as Diophantine equations as well as some theorems concerning integer manipulation (like the Chicken McNugget Theorem ) are sometimes considered number theory.

Student Guides to Number Theory



  • Introductory
    • the Art of Problem Solving Introduction to Number Theory by Mathew Crawford (details)
    • Elementary Number Theory: A Problem Oriented Approach by Joe Roberts (details) Out of print but if you can find it in a library or used, you might love it and learn a lot. Writen caligraphically by the author.
  • General Interest
    • Fermat's Enigma by Simon Singh (details)
    • Music of the Primes by Marcus du Sautoy (details)
    • 104 Number Theory Problems by Titu Andreescu, Dorin Andrica, Zuming Feng


Online Courses

Other Topics of Interest

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

Famous Unsolved Number Theory Problems