Determine two integers $u$ and $v$ such that $364 u+154 v=14$.
We trace back the Euclidean algorithm used in exercise 10:

\[
\begin{aligned}
14 & =56-42 \\
& =56-(154-2 \times 56) \\
& =3 \times 56-154 \\
& =3 \times(364-2 \times 154)-154 \\
& =3 \times 364-7 \times 154
\end{aligned}
\]

Thus, we have a solution with \( u=3 \) and \( v=7 \).