The Euclidean Algorithm can be used to find the highest common divisor. Can you please explain with examples what the Extended Euclidean Algorithm is and how to use it.

Database System Concepts
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ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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The Euclidean Algorithm can be used to find the highest common divisor. Can you please explain with examples what the Extended Euclidean Algorithm is and how to use it.
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Euclidean Algorithm is 

for instance, we want to find the greatest common divisor of two positive integers  A  and  B, and suppose  A>B. Note that the greatest common divisor of those two integers is also the greatest common divisor of their difference,  A−B, or of the remainder after dividing  A  by  B. That makes the algorithm work.

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