numbers form a -multimagic series if the sum of their th powers is the Magic Constant of degree for every , ..., . The following table gives the number of -multimagic series of given orders (Kraitchik 1942).

2 | 2 | ||

3 | 8 | ||

4 | 86 | 2 | 2 |

5 | 1,394 | 8 | 2 |

6 | 0 | 98 | 0 |

7 | 0 | 1,844 | 0 |

8 | 0 | 38,039 | 115 |

9 | 0 | 0 | 41 |

10 | 0 | 0 | 0 |

11 | 0 | 0 | 961 |

**References**

Kraitchik, M. ``Multimagic Squares.'' §7.10 in *Mathematical Recreations.* New York: W. W. Norton, pp. 176-178, 1942.

© 1996-9

1999-05-26