The 2-1 equation

(1) |

There are no known 3-1, 3-2, or 3-3 solutions.

There are no known 4-1, 4-2, 4-3, or 4-4 solutions.

There are no known 5-1, 5-2, 5-3, 5-4, or 5-5 solutions.

There are no known 6-1, 6-2, 6-3, 6-4, or 6-5 solutions. The smallest 6-6 solution is

(2) |

There are no known 7-1, 7-2, 7-3, 7-4, or 7-5 solutions.

There are no known 8-1, 8-2, 8-3, 8-4, or 8-5 solutions.

There are no known 9-1, 9-2, 9-3, 9-4, or 9-5 solutions.

There are no known 10-1, 10-2, or 10-3 solutions. The smallest 10-4 solution is

(3) |

There are no known 11-1 or 11-2 solutions. The smallest 11-3 solution is

(4) |

(5) |

There is no known 12-1 solution. The smallest 12-2 solution is

(6) |

There are no known 13-1 or 14-1 solutions. The smallest 15-1 solution is

(7) |

**References**

Lander, L. J.; Parkin, T. R.; and Selfridge, J. L. ``A Survey of Equal Sums of Like Powers.'' *Math. Comput.*
**21**, 446-459, 1967.

Moessner, A. ``On Equal Sums of Like Powers.'' *Math. Student* **15**, 83-88, 1947.

Palamá, G. ``Diophantine Systems of the Type
(, 2, ..., ,
, , ..., ).'' *Scripta Math.* **19**, 132-134, 1953.

© 1996-9

1999-05-24