Notes in Number Theory

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About the notes

This set of number theory notes is intended for secondary school students. Interested students should read through each topic, and finish all the proofs (theorems and exercises) inside the notes.If you can figure out most of the proofs, you should expect yourself capable to represent your country in the International Mathematical Olympiad.

The notes should also be useful for Year 1 students taking a course in elementary number theory, because some exercise problems in the notes is quite difficult.

The notes includes the following topics:

  • Divisibility
  • Greatest common divisor
  • Prime numbers
  • Fundamental theorem of arithmetic (i.e. prime factorization)
  • Congruence relations (or modular arithmetic)

Readers should note that Diophantine equation is NOT included in the notes. You should find materials of this topic elsewhere.

If you have finished reading the notes, you should consider taking a full course in elementary number theory, such as http://ocw.mit.edu/courses/mathematics/18-781-theory-of-numbers-spring-2012/lecture-notes/.