Chapter 1
Arithmetic


  1. Divisors and multiples

  2. Euclid's algorithm

  3. Linear diophantine equations

  4. Prime numbers

  5. Factorization

  6. Exercises

  7. Summary of Chapter 1

In this chapter we study properties of the set Z of integers. We deal mainly with its multiplicative structure and discuss notions such as the greatest common divisor (gcd) and the least common multiple (lcm) of two (or more) integers.

Section 1.1
Divisors and Multiples
  1. Divisors
  2. Division with remainder
  3. Common divisors
  4. Common multiples
Section 1.2
Euclid's algorithm
  1. Euclid's algorithm
  2. Extended Euclidean algorithm
  3. Characterization of gcd
  4. Relatively prime
Section 1.3
Linear diophantine equations
  1. Homogeneous equation
  2. Linear equation
Section 1.4
Prime numbers
  1. The notion
  2. Eratosthenes' sieve
  3. Characterization of primes
Section 1.5
Factorization
  1. The notion
  2. Gcd and lcm