This section mainly centers on Euclid's Lemma and its corallaries. The actual proof of the Lemma is neat, however, what is more interesting to me is the usefulness of the lemma in proving other things. In the book it talks about several corallaries and uses the lemma to prove them. Something else that caught my eye was in the proof of theorem 11.16. Two results for 'c' were found and both were substituted in the same equation allowing us to pull out the 'ab' necessary to show that ab|c. I thought that was clever and something I would have missed on my way through the proof for sure.
This section was fairly short and easy for me to understand. At first I had to reason in my mind what it meant for two numbers to have a gcd of 1. Actually, I guess I still don't quite understand that set of numbers. It states that the two numbers are integers, so it seems like to have a gcd of 1 and all the coeffecients to be integers as well, the two numbers (integers also) would need to be zero and one or some combination of negative and postive integers. I would like it if we could go over some examples of integers with gcd of 1 just so I can have a concrete understanding.
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