| # Modular Multiplicative Inverse | |
| ## Description | |
| Given coprime positive integers $a$ and $m$, compute the canonical multiplicative inverse of $a$ modulo $m$. | |
| ## Input | |
| The function receives $a$ and modulus $m$. | |
| ## Output | |
| Return the unique $x$ in $[0,m)$ such that $ax \equiv 1 \pmod m$. | |
| ## Constraints | |
| - $1 < m$. | |
| - $0 < a < m$. | |
| - $\gcd(a,m)=1$. | |
| ## Source | |
| Classical extended-Euclidean-algorithm problem reconstructed from the verified C artifact. | |