I guess the thing I am most confused about is how we factor the numbers into smaller primes. The example of the basic principle on page 183 starts by saying 9398^2 = 5^5 * 19 (mod 3837523) but I don't really see how they got that or how I would factor an even bigger number. I believe, upon finishing the chapter, that they give the explanation on page 185 but I didn't quite see how it all related. I'm not sure where this equation of in+sqrt(in) + j^2 came from or how it helps us factor n into smaller primes.
The most interesting part of this section for me was the idea of using matrices. I enjoy linear algebra and I loved my Matrix Analysis class so I'm pretty eager to see additional applications of matrices. This matrix formed in this section must serve a purpose, although I have not successfully identified it yet. I understand how the matrix is formed, but I don't see where the linear independence comes in, or why we move to mod 2.
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