3.10, due on October 19

• The Jacobi Symbol part was a little shaky for me to understand. The whole thing just seems so "do it the way you want to". I understand the process of using the 5 rules of the Jacobi Symbols to reduce and flip the fractions, but the problem for me stems all the way back to the face that (2/n) = +1 is n is congruent to 1 or 7 mod 8 and = -1 if n is congruent to 3 or 5 mod 8. I'm not sure whether I'm supposed to be able to calculate that to see it or if I'm just supposed to take it as fact because its part of a theorem.
• I'm not too sure about the Legendre symbol either. We went over it briefly in class, so I recognized it when I saw it, but I'm stuck on it for the same reason as being stuck on the Jacobi symbol. All of the properties just seems so random that I think I may have a hard time remembering them all.