The most difficult part of the section for me was the end of the section. I don't really understand how the book came to the conclusion that if d divides b than [a]x=[b] has solutions in Zn. I also don't know why there would be d number of solutions. I figure that those proofs will be really difficult for me to come up with. I also didn't really understand why it works to change things Zn to Z and what that means (technique i from the basic techniques for proving statements in Zn).
After reading section 2.2 and doing the homework I could tell that the book was leading us to think more about Z for prime numbers. I was really excited to get into section 2.3 to discover what the properties are for congruence classes for primes since they were hinting at certain things so strongly. The most interesting part of the section was the proof of theorem of 2.8. First off, method one that they used to prove this theorem where they change Zn to Z is really clever and I had no idea that was possible. Then the arithmetic and the tricks used in the proof are really clever and helped me think more about tricks to use for proofs.
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