Summary of Chapter 1

Overview of sections

1. Divisors and multiples
2. Euclid's algorithm
3. Linear diophantine equations
4. Prime numbers
5. Factorization
6. Exercises

Overview of contents

Chapter 1 is about multiplication and division of integers. We consider the following topics:

• Division with remainder: determine the quotient and remainder.
• Euclid's algorithm for finding the gcd.
• The extended Euclidean algorithm for expressing the gcd of a and b in the form xa + yb.
• Prime numbers: the building blocks of integers. We discuss:
  • There are infinitely many prime numbers.
  • Using Eratosthenes' sieve you can determine all the primes less than a given number.
  • Prime factorization: Any number is the product of primes; this factorization is unique (up to the order).