MEMO 2017 pojedinačno problem 2
Let be an integer. A labelling of the vertices, the sides and the interior of a regular -gon by distinct integers is called memorable if the following conditions hold:
(a) Each side has a label that is the arithmetic mean of the labels of its endpoints.
(b) The interior of the -gon has a label that is the arithmetic mean of the labels of all the vertices.
Determine all integers for which there exists a memorable labelling of a regular -gon consisting of consecutive integers.