In this video we cover the following concepts:

Divides - We say \(d\) divides \(n\) if there exists an integer \(k\) such that \(n = d\cdot k\). We write \(d \mid n\).

Well-ordering principle - Let \(S \subseteq \mathbb{N}\) and assume \(S \neq \emptyset\). Then \(S\) has a least element.

Division algorithm - Let \(a\) and \(b\) be integers with \(a\neq 0\). Then there exists unique integers \(q\) and \(r\) such that

  1. \(b = qa + r\),
  2. \(0\leq r < \lvert a \rvert\).

Prime - a number \(n\geq 2\) is prime if its only positive divisors are \(1\) and \(n\). Otherwise, \(n\) is called composite.

Products of primes - every integer \(n\geq 2\) can be written as a product of primes.