Difficult: A lot of section 1 was pretty basic, but could you go over how to do the "divides" and "does not divide" symbols in Latex? I don't know if you just use the absolute value sign, or if that'll mess up Latex. Also, example (result) 4.8 in the book made sense, but the proof didn't seem intuitive. It didn't seem direct or contrapositve, so maybe could you show an example like that in class? (For every integer n>=7, there exist positive integers a and b such that n=2a+3b.)
Congruence was a little tougher. These will probably just take a lot of practice and learning the definitions to get those proofs through smoothly.
Interesting: It's really cool, because I often thought about the concept of congruent/modulo numbers, but never knew that they had a name in mathematics. It's also really cool that you can prove really obscure things that I would have never guessed were true using these proofs. The even/odd proofs were pretty obvious, but I never knew that if x isn't a multiple of three, then x^2-1 is always a multiple of three. Just really interesting!
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