1. I simply could not follow the extended Euclidean algorithm. I am not sure if it is because I don't understand the operation, but even after going over their example several times, I am having a hard time conceptualizing it or even understanding the steps and logic behind each operation. Why is it useful to us?
I had an easier time understanding the basic idea behind congruences, but I guess I don't yet see how it will be helpful to us in this course or in real life. I am sure that will become more obvious as the class goes on.
I had a hard time understanding how they solved the last example on pg. 73. How is 4/11111 the same as working with mod 12345?
I also don't completely understand how to work with fractions. Is there a logical way to keep track of when I need certain integers to be relatively prime or when their gcd(a,n)=1.
2. When we studied congruences in Math290 I was curious as to what discipline or sector of math to which it is helpful. I am excited to see how it is a part of cryptography and keeping messages safe.
I think my favorite part was in the second example on page 73 when they show how 7 is congruent to 18 which is congruent to 29 which is congruent to 40 and as we find all the different congruencies it makes it possible for us to divide. It's an interesting way to think and sort of reminds me of how our number system is base 10, but how you can do math in different bases.
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