### Abstract

We deduce an accurate formula for the number of solutions of the linear equation in generators of finite Carlitz modules, and the equation always has solutions except for some cases. Therefore, we have a criterion for the existence of the solutions of the linear equation. Moreover, we have a similar result in normal bases when we apply our main theorem to a special case.

Original language | English |
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Pages (from-to) | 2191-2200 |

Number of pages | 10 |

Journal | Proceedings of the American Mathematical Society |

Volume | 137 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2009 Jul 1 |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Hsu, C. N., & Nan, T. T. (2009). On the number of solutions of the linear equation in finite carlitz modules.

*Proceedings of the American Mathematical Society*,*137*(7), 2191-2200. https://doi.org/10.1090/S0002-9939-09-09747-0