Past exam of the year 1 of the computer science course of the University of Oxford / 2021 / Discrete mathematics, continuous mathematics, and probability / 1 / b / i / Solution

The Euclidean algorithm givesso $\gcd (754,91)=\gcd (26,91)=13$. Since $13\mid 39$, the criterion for a linear congruence guarantees a solution. One can also exhibit it directly: $26\cdot 5+91(-1)=39$, or in the original coefficients,Thus $x=5$ is a solution, with an explicit Bézout coefficient certificate.