A multimagic square such that the first, second, third, and fourth powers of the elements all yield magic squares is known as a tetramagic square. The first known tetramagic square was constructed by Christian Boyer and André Viricel in May 2001. It is of order 512 (Boyer 2001).
Tetramagic Square
See also
Bimagic Square, Multimagic Square, Pentamagic Square, Trimagic SquareExplore with Wolfram|Alpha
References
Boyer, C. "Les premiers carrés tétra et pentamagiques." Pour La Science, No. 286, pp. 98-102, Aug. 2001.Boyer, C. "Tetramagic Squares and Pentamagic Squares." http://www.multimagie.com/English/Tetra-penta.htm.Referenced on Wolfram|Alpha
Tetramagic SquareCite this as:
Weisstein, Eric W. "Tetramagic Square." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TetramagicSquare.html