Question 7
In space, let $D$ be a convex polyhedron such that an even number of edges meets at each vertex. Choose one face $F$ of $D$. Assign a positive integer to each edge, with the property that for every face other than $F$, the sum of the integers on its boundary edges is divisible by $2024$. Prove that the sum on the boundary edges of $F$ is also a positive integer divisible by $2024$.