I know you can write gcd of two numbers as a linear combination of two numbers, but my question is what do we achieve by doing that? is there any significance of writing gcd as linear combination? does that give us some more interesting info about gcd and those two numbers?
2026-02-22 19:54:29.1771790069
GCD as linear combination of two numbers
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That result is known as Bézout's identity and it is very useful to solve many problems in number theory as for example the calculation of the modular inverse.
Take also a look here What is the importance of Bézout's identity?