Difficult: The calculations used to find the a and b such that ax+by=d will be difficult to remember, even if they are just based on the Euclidean Algorithm. I believe this works because I can see it, but I do not readily see how it works. I think I can see the connection to the discussion of using primes to generate cyphers from chapter 1, but of course I am not sure. Would it be harder to find a and b if d is large? Or maybe if a and b are large? The examples work out quickly, thought the numbers involved are not small. How can we be sure to increase (or decrease) the number of steps in the Euclidean algorithm to increase (or decrease) the complexity of this calculation?

Reflective: Still using some ring theory, though I don't think I've ever used fractions in a modulus problem before. It's pretty interesting to me how that works, just interpreting the fraction as an inverse of some other number.