Daily Prep 3B -- MTH 350-01

--- tags: mth350, dailyprep --- # Daily Prep 3B -- MTH 350-01 ## Overview We continue our study of the greatest common divisor (GCD) by applying the Euclidean and Extended Euclidean Algorithms to arrive at some useful and important theorems about GCDs. **Bezout's Identity** (Theorem 3.9) is foremost among these; Theorem 3.10 and Corollary 3.11 are related and perhaps even more useful. We'll focus on understanding proofs of these three results in class, as well as Theorem 3.15 which gives an alternative definition of the GCD that's very useful moving forward. ## Learning objectives **Basic Learning Objectives:** *Before* our class meeting, use the Resources listed below to learn all of the following. You should be reasonably fluent with all of these tasks prior to our meeting; we will field questions on these, but they will not be retaught. - State the definition of the greatest common divisor of two integers. - State the following results and use them to draw conclusions or restate information: Theorem 3.9 (Bezout's Identity), Theorem 3.10, Corollary 3.11, Theorem 3.14, and Theorem 3.15. **Advanced Learning Objectives:** *During and after* our class meeting, we will work on learning the following. Fluency with these is not required prior to class. - Explain line-by-line a proof of Theorem 3.10. - Explain how Corollary 3.11 follows from Theorem 3.10. - Explain line-by-line a proof of Theorem 3.15. - Construct proofs of other results involving the GCD. ## Resources for learning **Reading:** Read through the remainder of Investigation 3 (pp. 39--42) in the textbook. No videos this time, although you're welcome to search for those on your own if you want. ## Exercises The exercises for this Daily Prep are found on the Google Form: https://docs.google.com/forms/d/e/1FAIpQLSd2mDs--9EtJwbFfhrKegotjVEklGYQUMr3hjrhfRm-qWTRQA/viewform ## Submission and grading To submit your work, simply submit the Google Form. You will receive a receipt via email to confirm your submission. (Look in your spam folders if you do not see the receipt.) A **Pass** mark is given if the Daily Prep is turned in before its deadline and if each item on the Daily Prep has a response that represents a good faith effort to be right. **Mistakes are not penalized**. A **No Pass** is given if an item is left blank (even accidentally), has an answer but it shows insufficient effort (including responses like "I don't know"), or if the Daily Prep is late.