In this video, we learn how to find the gcd of two integers A and B, and then compute integers u and v such that uA + vB = gcd(A,B). Link to the previous video (Euclidean Algorithm and GCD): • Abstract Algebra: Usin...
This video helped SO MUCH! With all classes being online, my prof is no longer doing lectures how he used to and this topic was poorly executed. I'm glad a classmate found this video!
I think the general solutions to the problem are u = 7 + 31k and v = -16 - 71k. There are infinitely many solutions to this because after finding the lcm, there's no limit to the amount of factors that lead to a difference of 10.
It seems a monstrously complicated way of doing it. There are so many operations necessary for even a fairly simple calculation, and of course the more separate operations you have to do the more likely you are (anyway, I am!) to make an error.
This is not a calculation that you have to do for each and every solution. Once you get the 1st solution (shown in the video) you can use that to generate most or all of the rest. So it is a practical method. In this case, this solution is enough to generate all of the others of the form u = 7 + 31k and v = -16 - 71k. And there's infinitely many of those.
