These are notes on elementary number theory; that is, the part of number theory which does not involves methods from abstract algebra or complex variables.

The first link in each item is to a Web page; the second is to a PDF file. Use the PDF if you want to print it. There are videos for some of the sections, but they don't cover everything in the printed notes.

These notes have been revised at various times (2008, 2011, 2016).

- The ring of integers. [PDF]
- Sums and products.
[PDF]

Video: Sums (17 minutes, 20 MB)

Video: Products (23 minutes, 24 MB) - Binomial coefficients. [PDF]
- Induction. [PDF]
- Fibonacci numbers. [PDF]
- Divisibility and the
Division Algorithm.
[PDF]

Video: Divisibility and the Division Algorithm (37 minutes, 44 MB) - Prime numbers.
[PDF]

Video: Prime numbers (33 minutes, 38 MB) - Greatest common divisors. [PDF]
- The Extended Euclidean Algorithm. [PDF]
- The Fundamental Theorem of Arithmetic. [PDF]
- Elementary factoring methods; Fermat factorization.
[PDF]

Video: Fermat factorization (15 minutes, 18 MB) - Linear Diophantine equations. [PDF]
- Congruences and modular arithmetic. [PDF]
- The day-of-the-week algorithm. [PDF]
- Solving linear congruences (one and two variables). [PDF]
- The Chinese Remainder Theorem. [PDF]
- Systems of linear congruences. [PDF]
- Prime power congruences. [PDF]
- Wilson's Theorem and Fermat's Theorem. [PDF]
- Euler's Theorem; the Euler phi function.
[PDF]

Euler's theorem; the Euler phi-function (23 minutes, 27 MB) - Properties of the Euler phi function; multiplicative functions; Dirichlet products; Möbius inversion. [PDF]
- The sum and number of divisors functions. [PDF]
- Perfect numbers and Mersenne primes. [PDF]
- Character and block ciphers. [PDF]
- Exponential ciphers; the RSA algorithm. [PDF]
- Quadratic residues. [PDF]
- Quadratic reciprocity. [PDF]
- The Jacobi symbol. [PDF]
- Decimal and base-b fractions. [PDF]
- Finite continued fractions. [PDF]
- Infinite continued fractions. [PDF]
- Periodic continued fractions. [PDF]
- Approximation by rationals. [PDF]