Here is a nice like theorem that I wish I would have noticed for the homework that was due on Monday. That basically solves two of the problems right there. It is interesting that we can figure out that numbers can be factored without ever actually factoring them.
It is also interesting in the fermat primality test that "then n is probably prime" so even with our test we arent exactly sure about what is going on. Also how likely is very likely that its true? Are we talking like usually, 55%? Or like very probably like 95%?
Is the Miller Rabin test really saying that you just randomly choose one of the numbers and then see if it works and if not then try another? That seems like an inefficient way first of all, and second does the randomization help in any way? Also what does it mean when they reach mod 1 but not all at the same time?
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