Queens on non-square tori (Q5936800)

A problem analogous to the classical one concerning queens on a chessboard is treated. Here the chessboard is not a square in the plane, but is drawn on the torus. It is of type \(n\times m\), where \(m< n\). The problem is to determine the maximum number of pairwise non-attacking queens which may be placed on such a chessboard. It is proved that except the case \(m=3\), \(n=6\) this number is equal to the greatest common divisor of the numbers \(m\) and \(n\).