1.1-1.2 and 3.1, Due on September 1

1. The most difficult part of the material for me was the Theorem on page 68. The theorem makes sense to me but I got lost in the proof. I understand how it related to the Euclidean Algorithm but the numerous variables and their representations confused me. I think seeing it a second time in class will be helpful.
2. One thing that I thought of when I read the first two sections was in regards to online security. In the last two years or so I have often been asked to identify or decipher a message while typing in my password on certain web pages. When I check my Gmail I am asked to type in a 'word verification' before I can sign in. These words are often nonsense and upon reading this section I am wondering if these 'word verifications' relate to password security. Someone told me that they are meant to make sure a human is at the computer and not some computer trying to hack into my email. I don't know what the answer is but I do believe it has to do with securing private information online.