Problem

Source: Kyiv City MO 2025 Round 1, Problem 8.3

Tags: geometry, combinatorial geometry



What's the smallest positive integer \( n > 3 \), for which there does not exist a (not necessarily convex) \( n \)-gon such that all its diagonals have equal lengths? A diagonal of any polygon is defined as a segment connecting any two non-adjacent vertices of the polygon. Proposed by Anton Trygub