Tuesday, 21 October 2014

number theory - How to find integer linear combination

The question said:



Use the Euclidean Algorithm to find gcd $(1207,569)$ and write $(1207,569)$ as an integer linear combination of $1207$ and $569$



I proceeded as follows:



$$ 12007 = 569(2) +69$$




$$569 = 69(8) +17$$



$$69 = 17(4) +1$$



$$17 = 1(17) + 0$$



Thus the gcd = 1



The part I am having problems with is how calculate and write it was a linear combination. Can someone help?

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