1. This section had many properties in it relating integer arithmetic to integer(mod n) arithmetic. I think the most difficult one for me to conceptualize was property 5 for modulo arithmetic: For each [a] in the integers(mod n), the equation [a]+X=[0] has a solution in the integers(mod n). I had to think a bit about what "X" would be, and I finally realized that it would be an equivalence class, more specifically it would be the equivalence class of [-a].
2. The most interesting part of the material was that you could take a large arithmetic problem regarding the integers in modulo n, and you can either compute the modulo 10 arithmetic and then simplify your answer to modulo n, OR you could simplify along the way so you don't end up with a huge number to reduce to modulo n.
Example (in modulo 3): ([4]+[7])*[2] = [22] = [19] = ... = [4] = [1] vs. ([4]+[7])*[2] = ([1]+[1])*[2] = [4] = [1]
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