1. The part that was the most difficult for me to understand was the chapter on greatest common factors. I know what they are, and I have used the Euclidean algorithm before to find them, but Lemma 1.7 is something I haven't seen before, and it took a careful reading to understand what it was saying and how it applied.
2. I thought the well-ordering axiom and its uses were really cool. It's similar to the Axiom of Completeness in Math 341 for the real numbers; it's something that intuitively makes sense but that I didn't really think about until we used it to prove lots of other theorems. I also enjoyed reading about primes; I have seen all of the results in that chapter before, but it was good to see them again.
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