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.
- Importantly, we use this notion to introduce the key concept of Relatively Prime, and prove some facts about this concept.
Finally, we have Exercises.
