Problem

Source: 2024 Vietnam National Olympiad - Problem 7

Tags: number theory, combinatorics



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 $2024$.