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Modified Euclid's Algorithm

  1. Oct 29, 2009 #1
    1. The problem statement, all variables and given/known data

    Let a = 47 and b = 41. Use the modified euclid's algorithm to find integers x and y such that [tex]ax+by=1[/tex].

    Here's the solution to this problem:

    http://img203.imageshack.us/img203/6044/19152421.gif [Broken]


    3. The attempt at a solution

    I don't understand how to workout the x and y columns. For example in the fourth row we can see that [tex]5=-6 \times 47+7 \times 41[/tex] works, but I don't see how they figured out x=-6 and y=7 in the first place.
    I'm revising for my exam and this is not a homework problem, so I appreciate it if anyone could explain to me what's going on here. :confused:
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
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