16.5

1. This section wasn't extremely difficult, but I would like to investigate what properties inverses in some field have when they are considered in an enclosing structure, like the ring Z.

2. We've talked a couple times about how there is no real notion of smallness when it comes to points on the curve E, and how it is for that reason that we can't use the same methods to attack the discrete logarithm problem for elliptic curves. At first I was tempted to say that we picked the wrong analogy and that comparing it to a discrete logarithm was guiding our intuition in the wrong direction, but I suppose it is the same problem if we used multiplicative notation instead of additive. Anyway, my point is that perhaps there is someway to define smallness based on certain properties, etc.