A magic square is said to be 
-multimagic if the square formed by replacing each element
by its 
th
power for 
,
2, ..., 
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 (1891). Tetramagic and pentamagic squares were constructed by Christian Boyer and André Viricel in 2001 (Boyer 2001).
