Given a table m×n, in each cell of which a number +1 or −1 is written. It is known that initially exactly one −1 is in the table, all the other numbers being +1. During a move, it is allowed to chose any cell containing −1, replace this −1 by 0, and simultaneously multiply all the numbers in the neighbouring cells by −1 (we say that two cells are neighbouring if they have a common side). Find all (m,n) for which using such moves one can obtain the table containing zeros only, regardless of the cell in which the initial −1 stands. algorithmcombinatorics unsolvedcombinatorics