Use the Euclidean algorithm to find integers x and y such that 164x+37y=1. Note that while there are many pairs of integers x and y that satisfy this equation, there is only one pair that comes from using the Euclidean algorithm.
I was able to find a solution without using the Euclidean algorithm but I'm struggling to use the algorithm to solve it so I'd really appreciate some help. Thanks in advance!!
The Euclidean algorithm gives the solution (x,y) = (-30,133). You can check that 164(-30) + 37(133) = 1.
This is one of the BEST videos that I have seen on the explanation of Extended Euclidean Algorithm, Watch it step by step very slowly and view it several times. I think you will evetually understand it. Good luck.