1. I followed the examples for the Chinese Remainder Theorem, but I got lost at the Lemma and its proof in Section 3.4. I understand its usefulness in understanding the Chinese Remainder Theorem, but I don't get the proof, or why they start the proof where they did.
2. I really thought Section 3.5 was interesting. It combines what I know about binary with what I know about congruences to find answers to congruences, even when working with large numbers. This seems like it will be very useful going forward. The only part I didn't understand was the sentence "If we want to compute a^b (mod n), we can do it with at most 2 log2(b) multiplications.
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