In the space, there is a convex polyhedron D such that for every vertex of D, there are an even number of edges passing through that vertex. We choose a face F of D. Then we assign each edge of D a positive integer such that for all faces of D different from F, the sum of the numbers assigned on the edges of that face is a positive integer divisible by 2024. Prove that the sum of the numbers assigned on the edges of F is also a positive integer divisible by 2024. number theorycombinatorics