A magic square is said to be p-multimagic if the square formed by replacing each element by its kth power for k = 1, 2, ..., p is also magic. A 2-multimagic square is called bimagic, a 3-multimagic square is called trimagic, a 4-multimagic square is called tetramagic, a 5-multimagic square is called pentamagic, and so on. The first known bimagic square had order eight and was constructed by Pfefferman. Tetramagic and pentamagic squares were constructed by Christian Boyer and André Viricel in 2001.

bimagic square | magic square | pentamagic square | tetramagic square | trimagic square