## Abstract

In this paper, we show that for almost all primes p there is an integer solution xε [2,p-1] to the congruence x^{x} ≡ x (mod p). The solutions can be interpretated as fixed points of the map x→x^{x} (mod p), and we study numerically and discuss some unexpected properties of the dynamical system associated with this map.

Original language | English |
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Pages (from-to) | 141-168 |

Number of pages | 28 |

Journal | Mathematical Research Letters |

Volume | 22 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2015 |

Externally published | Yes |

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