How can backwards operation of euclid algorithm prove Bezout identity ?
Note: Proof of Bezout's Lemma using Euclid's Algorithm backwards is quite difficult to understand
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Your post is quite terse. There are ways to improve it and reduce the chance of having your Question treated as a duplicate. On first glance it would seem you know or have been told that we can prove Bezout's identity by reversing (unwinding) the steps of Euclid's algorithm that find the GCD of two integers. At one extreme you might see that this works in most cases but have a doubt that it would always work; at the other extreme you might not understand what it means to proceed in this fashion. Showing an example of the process as you understand it will help Readers respond cogently. – hardmath Apr 05 '20 at 14:39
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See https://en.wikipedia.org/wiki/Euclidean_algorithm#Matrix_method – lhf Apr 05 '20 at 14:43
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@lhf Should it be https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm#Proof instead ? – kevin Apr 06 '20 at 01:21
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@kevin, both links are good. – lhf Apr 06 '20 at 09:54