The most difficult part of the material was by far the notation for congruence of Integers. The concept is not exactly easy to understand, and the reason it's usefulness is also not as easy to understand. They might as well write n | (a-b), instead of making a=b (mod n).
The most interesting part was where they showed that how everything divisible by 2 can only have 0 or 1 as a remainder, and then showed that it was similar for n = 3q + 1 or n = 4q + 1, with the number of possible remainders increasing each time. I look forward to exploring this in more detail in chapter 11.
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