# Online Bezout coefficients calculator

For a given $a, b \in \mathbb{Z}^{*}$, find $u, v \in \mathbb{Z}$ verifying : $$au+bv=\gcd(a, b)$$
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## What is Bezout coefficients ?

Let $a, b \in \mathbb{Z}^{*}$, Bézout's identity states that : $$\gcd(a, b) = d \implies \exists (u_0, v_0) \in \mathbb{Z}^{2} \ : \ au_0+bv_0=d$$ And the set of solutions of $au+bv=d$ is : $$S=\left\{\left(u_0 + k \frac{b}{d}, v_0 - k\frac{a}{d}\right) \ \middle| \ k \in \mathbb{Z} \right\}$$
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