Question 64
In a $n \times n$ chart, two cells of the chart are called adjacent if they have a common side. At the origin, there is a number $+1$ in every cell. An operation means that: one can choose a cell, and change the signs of all the numbers which are in the adjacent cells of it (doesn't change the sign of the number in it). Find all integers $n \ge 2$, for which, after finitely many suitable operations, the numbers in all cells are changed to $-1$.