Bézout coefficient ($ax+by=\gcd (a,b)$)

Bézout coefficients for integers $a,b$ are integers $x,y$ satisfying Bézout's identity $ax+by=\gcd (a,b)$. The extended Euclidean algorithm computes one pair. They need not be unique: both $(x,y)=(7,-2)$ and $(-10,3)$ work for $(a,b)=(5,17)$, since $35-34=1$ and $-50+51=1$.