Summary: Basic Integer Division Here are some of the main results of this chapter. The Division Algorithm is a foundational result. We use it immediately to prove a well-known fact in Proposition 2.1.4. Note that the proof in Subsection 2.1.2 uses the Well-Ordering Principle. We review Common Divisors and the greatest common divisor, introducing its characterization in Theorem 2.2.4. The Euclidean algorithm is foundational for this task; see Example 2.3.1 for a good example. Then we use the previous section’s work to prove the Bezout identity. We do several examples. Importantly, we use this notion to introduce the key concept of Relatively Prime, and prove some facts about this concept. Finally, we have Exercises.