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Multimagic cube
In mathematics, a ''P''-multimagic cube is a magic cube that remains magic even if all its numbers are replaced by their ''k''-th power for 1 ≤ ''k'' ≤ ''P''. Thus, a magic cube is bimagic when it is 2-multimagic, and trimagic when it is 3-multimagic, tetramagic when it is 4-multimagic. A ''P''-multimagic cube is said to be semi-perfect if the ''k''-th power cubes are perfect for 1 ≤ ''k'' < ''P'', and the ''P''-th power cube is semiperfect. If all ''P'' of the power cubes are perfect, the multimagic cube is said to be perfect.
The first known example of a bimagic cube was given by John Hendricks in 2000; it is a semiperfect cube of order 25 and magic constant 195325. In 2003, C. Bower discovered two semi-perfect bimagic cubes of order 16, and a perfect bimagic cube of order 32.
MathWorld reports that only two trimagic cubes are known, discovered by C. Bower in 2003; a semiperfect cube of order 64 and a perfect cube of order 256. It also reports that he discovered the only two known tetramagic cubes, a semiperfect cube of order 1024, and perfect cube of order 8192.
== References ==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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