The conversation between human and AI assistant.
What is the proof of Euclid's algorithm?
That makes sense. Is there any other way to prove the algorithm?
Yes, there is another way to prove the algorithm known as the extended Euclidean algorithm. This algorithm not only finds the greatest common divisor of two numbers, but also finds a way to represent it as a linear combination of the two numbers. This proof uses the concept of extended GCD and Bezout's identity.