MathDB

Real numbers on vertices of polygon

Source: Kvant Magazine No. 2 2023 M2734

April 19, 2023

combinatoricsnumber theory

Problem Statement

Real numbers are placed at the vertices of an

n{}

-gon. On each side, we write the sum of the numbers on its endpoints. For which

n{}

is it possible that the numbers on the sides form a permutation of

1, 2, 3,\ldots , n

?
From the folklore