So I know when two integers are relatively prime, their greatest common divisor is $1$ and it can we be written as a linear combination as: $1 = am + nb.$ But how would I prove the existence of these integers a and b?
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1use the extended Euclidean algorithm – J. W. Tanner Nov 08 '19 at 01:53
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Is that working backwards from the Euclidean algorithm? – Nov 08 '19 at 01:58
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see this question – J. W. Tanner Nov 08 '19 at 02:00
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1Scale the Bezout identity $,m a + n b = 1,$ by $,x,$ to get $, (xm) a + (xn) b = x\ \ $ – Bill Dubuque Nov 08 '19 at 02:26