A tetramagic square is a magic square where if all values are raised to the power 2,3 and 4 the result is still a magic
square (on the left). The first tetramagic square found was with an order
of 512, which was discovered by Christian Boyer and André Viricel in 2001.
Pentamagic squares and all the others in the series follow a similar
pattern (on the right). As long as a magic square squared to the k-th
power can also be a magic square for all the powers beneath it (except
0), then it is called a
multimagic square to the k-th power. The first pentamagic
square found was of the order 1024 constructed by Christian Boyer and
André Viricel in 2001, however a smaller pentamagic square of order 729
was discovered in 2003 by Li Wen.
