# Euler’s conjecture

In 1769, Leonhard Euler conjectured that for $$ there is no set of positive integers ${a}_{1},\mathrm{\dots},{a}_{k}$ such that

$$\sum _{i=1}^{k}a_{i}{}^{n}={m}^{n},$$ |

where $m$ is an integer. Lander and Parkin in 1966 disproved the conjecture with this $k=4,n=5$ counterexample: ${27}^{5}+{84}^{5}+{110}^{5}+{133}^{5}={144}^{5}$. More counterexamples have been discovered since then.

Title | Euler’s conjecture |
---|---|

Canonical name | EulersConjecture |

Date of creation | 2013-03-22 16:25:43 |

Last modified on | 2013-03-22 16:25:43 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 7 |

Author | PrimeFan (13766) |

Entry type | Conjecture |

Classification | msc 11B13 |

Classification | msc 11D41 |

Synonym | Euler conjecture^{} |