1) I honestly don't really understand the proof for format's theorem but I think it is really cool how it works and how it is so helpful for us to evaluate somewhat complicated expressions in mod(n). I am also not completely understanding the general idea of Euler's theorem. What is that notation on pg. (81) half-way down?
2) I love learning all of these new ways to re-write expressions and magically simplify. I also think it is cool that such ancient discoveries have proved to be so useful in cryptography and with computers. No longer is it just cool for math-sakes. It actually has application.
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