Let $n\geq 3$ be a natural number and Consider the following game:

Correspond an integer to each vertices of an equiangular polygon (at least two of the numbers are unequal).

(1) Replace the number of each vertices with the number obtained by the sum of its neighborhood numbers minus its own number.

This gives us a new equiangular polygon with an integer corresponded to each of its vertices.

Again do as in (1) and Continue the progress.

Let $A$ be the set containing the numbers corresponded to vertices of this polygon in this (infinite) process. Now the question is:

what are the possible values of $n$ if we want $A$ to be a bounded set of integers!?

Let $n\geq 3$ be a natural number and Consider the following game:

Correspond an integer to each vertices of an equiangular polygon (at least two of the numbers are unequal).

(1) Replace the number of each vertices with the number obtained by the sum of its neighborhood numbers minus its own number. (Edit: Do this for all vertices at once, not one by one)

This gives us a new equiangular polygon with an integer corresponded to each of its vertices.

Again do as in (1) and Continue the progress.

Let $A$ be the set containing the numbers corresponded to vertices of this polygon in this (infinite) process. Now the question is:

what are the possible values of $n$ if we want $A$ to be a bounded set of integers!?