Saturday, September 11, 2010

#8: Lecture 8, due September 12th

Difficult- I think I am getting confused between the equations and the solutions. Okay so I think that if I'm following this correctly, in Zn if n is prime there is a unique solution to the equation ax=b, if a doesn't equal 0. But if n is not prime then only some equations have solutions? In that equation am I supposed to assume that a and b are classes since there are no bars? Because then in the next corollary the equation is back but with bars. Do they mean the same thing? Okay actually I think the second one might be different because it says a and n must be relatively prime.

Reflective- I found it interesting that in Zn if n is prime then there are special properties. I really think the Zn world is cool! When we were doing the tables in class I liked those a lot. Now it is interesting to see when n changes how properties and equations are formed, such as when n is prime. I also liked bringing the Euclidean algorithm in because I understand that so I can follow what that part is saying.

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