Euclidean Linear Combination

  • Thread starter Caldus
  • Start date
  • #1
106
0
I need to be able to plug in appropriate x and y values for:

154x + 260y = 4

I guess this is done by working the euclidean algorithm backwards. But how do you do that?
 

Answers and Replies

  • #2
jamesrc
Science Advisor
Gold Member
476
1
Well, it's been like forever and a day since I did problems like this, but I think it goes something like this:

154x + 260y = 4

260 = (1)*154 + 106
154 = (1)*106 + 48
106 = (2)*48 + 10
48 = (4)*10 + 8
10 = (1)*8 + 2
8 = (4)*2

4 = 2*2 = 2*(10-8) = 2*(10-(48-4*10))
= 10*10 - 2*48
= 10*(106 - 2*48) - 2*48
= 10*106 - 22*48
= 10*(260 - 154) - 22*(154-106)
= 10*260 - 32*154 + 22*106
= 10*260 - 32*154 + 22*(260-154)
= 32*260 - 54*154

so x = -54 and y = 32
 

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