Uniqueness of Extended Euclidean Algorithm

Given two integers $a$ and $b$, the Extended Euclidean algorithm calculates the $\gcd$ and the coefficients $x$ and $y$ of Bézout's identity: $ax+by=\gcd(a,b)$. These coefficients are not unique (see linked article).

The specific coefficients created by the algorithm satisfy these conditions: $$|x|<|\frac{b}{\gcd(a,b)}|$$ $$|y|<|\frac{a}{\gcd(a,b)}|$$

The Extended Euclidean Algorithm finds the solution closest to the origin.