A generalization of the usual n-queen problem is investigated. The n-by-n chessboard is regarded as the affine plane

�over the ring

�of integers modulo n. A superqueen at

�is defined to be able to attack another point

�if and only if

�

�

�

�or

�The problem of our main concern is to investigate whether there exists a configuration of n superqueens on

�for any n, none of which attacks each other.

n-queen problem, quadratic residue, elliptic curves.