Assignment 2

Probably the most difficult about this material was understanding how the proof of the theorem about ax + by = d, where d = gcd(a,b), works.  I know I have seen the proof before in 290, but the proof in this book for some reason isn't clicking for me, especially since the proof makes the theorem more general.  It makes sense to me that a and b must differ by a multiple of the gcd, but the proof seems to take a different route than I have before seen in proving this fact.

The part about primes was probably the most interesting to me because that was the part that I could understand the most.  The parts in chapter one about the basis for cryptography were interesting, but I wasn't quite sure how the mathematics would come into play, especially in talking about how the magnitude of the number n correlates to log(n).  The part about prime numbers and greatest common divisors reminded me about discussions we had in my first math education class about finding greatest common divisors and least common multiples.  For some reason, I found prime factorizations fascinating.  I was surprised by all of the methods for finding both the LCM and the GCD, especially in seeing how each method was related.  I'm curious to see if finding LCMs will show up in this class.