3.12, due on October 8

1. (Difficult): Continued fractions make sense but need solidifying. Can we see an example or two in class?
Also, I need to see an example of the simplified method at the end to understand what it's saying.

And out of curiosity (but less important to than my first two questions) I see that the quotients of computing the gcd is the same as the non-fraction part of the denominator, but why? And why are p-2 and p-1 ...defined as the 0's and 1's that they are?

2. (Reflection): So the algorithm for continued fraction is the floor of the original number x plus one over the floor of the reciprocal of the remainder(decimal part; what's left after discarding the floor of x) of x plus one over the floor of the reciprocal of the remainder of x plus...got it.

It will be interesting to see how we use this in cryptography.