Section 3.2.2 due October 19

I did not understand all of the equivalence statements on r(n) the number pairs that satisfy a^2 + b^2 =n. I do not really understand its importance, or how one could calculate it efficiently. I imagine it will make more sense in the next section.

I did find that p=1 mod 4 to be rather interesting. Something about mod 4 makes a huge difference and it seems to be stemming back to quadratic reciprocity. It sort of seems like a super odd or something like that. Most of the time, it seems that if something is odd verse even lots can be said, but this here is breaking odds into two categories and one does quite a bit, the other the opposite.