Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 1 / 1G / i / Solution

The linear Diophantine equation solvability criterion says that $ax+by=c$ has an integer solution exactly when $\gcd (a,b)$ divides $c$. The Euclidean algorithm givesThus $\gcd (1007,2314)=1$, which divides $37$. Therefore