I like algebra and I like modular arithmetic so I enjoyed this section. But, I didn't exactly follow all that transpired and I have a lot of questions. For example, the Proposition on page 86 requires p to be congruent to 3 mod 4, but I am wondering how often this if going to happen. Is this a frequent characteristics of primes? I'm also wondering how they got that (p+1)/4=3 in the example on page 87. I see that p=11 but I'm not sure why they broke it up in that way.
I enjoyed the last half of page 87 where the authors talk about breaking up the modular to get two different congruences, but I don't see it as too helpful since most of our mods in this section seem to be prime numbers. What is the connection there? I can see where this is going- factoring n- and I like it. I'm guessing that in certain instances of the RSA n is going to be factorable.
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