Question 58
Find all integers $n \ge 3$ such that one can write a number (not necessarily an integer) into each vertex of a regular $n$-gon in such a way that both following conditions are met:
(1) Whenever three consecutive vertices of the $n$-gon, taken clockwise, contain numbers $x, y$ and $z$, respectively, the equality $x = |y - z|$ holds;
(2) The sum of the numbers in all vertices of the $n$-gon is 1.
(1) Whenever three consecutive vertices of the $n$-gon, taken clockwise, contain numbers $x, y$ and $z$, respectively, the equality $x = |y - z|$ holds;
(2) The sum of the numbers in all vertices of the $n$-gon is 1.