3.9, due on October 15

1. (Difficult) I think I get one of the main points, is that if we can solve x^2 is congruent to y (mod n), then we can factor n, and vice versa.  I don't understand why talking about p being congruent to 3, mod 4 helps.  I didn't follow the example through, but I hope I will be able to complete the homework.
2. (Reflective) I think it is interesting when we find problems that are equivalent to problems we believe to be hard.  For example, the first sentence in the previous section.  It gives researchers different ways to approach what kind of ends up being the same problem.  I wonder if there has been any significant problems solved in this way?