Interesting: I have to admit that the proposition at the beginning was really interesting to me because it seems on the surface to be unrelated principles, and yet it's provable, and the proof isn't super complicated either. I don't know why, but it just amazes me sometimes how people can connect so many seemingly unrelated ideas to create theorems, etc. that really help advance our understanding of mathematics. I also thought the properties of the Jacobi symbol were interesting in the way that the authors applied them. I don't think I knew that Jacobi's ideas could really relate to reducing fractions, and yet it does! It also doesn't help that I don't remember how I really used the symbol before too though--maybe I knew and just forgot.
Difficult: I think it will definitely take practice to get used to using Legendre's and Jacobi's symbols in this way since I don't remember using it this way before (in fact, I really don't remember what I used it for before at all). So it will definitely take time for that to process.
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