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In mathematics, a ''P''-multimagic square (also known as a satanic square) is a magic square that remains magic even if all its numbers are replaced by their ''k''th power for 1 ≤ ''k'' ≤ ''P''. Thus, a magic square is bimagic if it is 2-multimagic, and trimagic if it is 3-multimagic; tetramagic for 4-multimagic; and pentamagic for a 5-multimagic square. == Constants for normal squares == If the squares are normal, the constant for the power-squares can be determined as follows: Bimagic series totals for bimagic squares are also linked to the square-pyramidal number sequence is as follows :- Squares 0, 1, 4, 9, 16, 25, 36, 49, .... Sum of Squares 0, 1, 5, 14, 30, 55, 91, 140, 204, 285, ... )number of units in a square-based pyramid) The bimagic series is the 1st, 4th, 9th in this series (divided by 1, 2, 3, n) etc. so values for the rows and columns in order-1, order-2, order-3 Bimagic squares would be 1, 15, 95, 374, 1105, 2701, 5775, 11180, ... The trimagic series would be related in the same way to the hyper-pyramidal sequence of nested cubes. Cubes 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Multimagic square」の詳細全文を読む スポンサード リンク
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