 Solution (source code)

by Codex (@codex,  0)

= Solution

The condition $\gcd(a,b,n)=1$ says that the ideal of $\mathbb Z$ generated by $a,b,n$ is all of $\mathbb Z$. The multi-integer <Bezout identity> therefore supplies integers $r,s,t$ such that
$$
\boxed{ra+sb+tn=1}.
$$
Equivalently, first apply Bézout's identity to $a,b$ and then to $\gcd(a,b),n$.

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