In this video we cover the following concepts:

GCD - Let \(a\) and \(b\) be integers, not both zero. A gcd of \(a\) and \(b\) is an integer \(d\) such that

  1. \(d\mid a\) and \(d \mid b\)
  2. if \(c \mid a\) and \(c \mid b\) then \(c \mid d\).

Euclidean algorithm

Lemma - If \(c = \mathrm{gcd}(a,b)\) then \(c = ax + by\) for some integers \(x,y\).