1) I didn't understand how the proof of Lemma 1.7 really proved that (a,b)=(b,r). Especially when they are using different values for the common divisor (c in the first, and e in the second).
2) I never thought about the fact that different numbers can have multiple prime factorizations depending on the negatives. I always just considered the case when there are only positive numbers. I also find the way that they prove some things to be very interesting and enlightening once I stare at it for a second, but I am just hoping that I can learn to do it on my own.
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