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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