Solution
= Solution
The <Euclidean algorithm> gives
$$
91=3\cdot26+13,\qquad26=2\cdot13,
$$
so $\gcd(754,91)=\gcd(26,91)=13$. Since $13\mid39$, the criterion for a <linear congruence> guarantees a solution. One can also exhibit it directly: $26\cdot5+91(-1)=39$, or in the original coefficients,
$$
754\cdot5+91(-47)=-507.
$$
Thus \b[$x=5$ is a solution], with an explicit <Bézout coefficient> certificate.