Find all integers n
Source: China Western Mathematical Olympiad 2013, problem 7
August 21, 2013
combinatorics unsolvedcombinatorics
Problem Statement
Label sides of a regular -gon in clockwise direction in order 1,2,..,n. Determine all integers n () satisfying the following conditions:
(1) non-intersecting diagonals in the -gon are selected, which subdivide the -gon into non-overlapping triangles;
(2) each of the chosen diagonals are labeled with an integer, such that the sum of labeled numbers on three sides of each triangles in (1) is equal to the others;