= Solution
The <Euclidean algorithm> gives
$$
\begin{aligned}
2392&=1748+644,\\
1748&=2\cdot644+460,\\
644&=460+184,\\
460&=2\cdot184+92,\\
184&=2\cdot92.
\end{aligned}
$$
The last nonzero remainder is \b[$g=92$]. Back-substitution produces its <Bézout coefficients>:
$$
\begin{aligned}
92&=460-2\cdot184\\
&=3\cdot460-2\cdot644\\
&=3\cdot1748-8\cdot644\\
&=-8\cdot2392+11\cdot1748.
\end{aligned}
$$
Thus \b[$(m,n)=(-8,11)$] is a requested pair. The final equality independently checks the calculation.
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