### Abstract

Let G_{n} be a linear recursive sequence of integers and P(y) be a polynomial with integer coefficients. In this paper we are given a survey on results on the solutions of diophantine equation G_{n} = P(y). We prove especially that if G_{n} is of order three such that its characteristic polynomial is irreducible and has a dominating root then there are only finitely many perfect powers in G_{n}.

Original language | English |
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Pages (from-to) | 81-96 |

Number of pages | 16 |

Journal | Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis |

Volume | 17 |

Issue number | 2 |

Publication status | Published - Dec 1 2001 |

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### Keywords

- Linear forms in logarithms of algebraic numbers, subspace theorem
- Linear recursive sequence, characteristic polynomial

### ASJC Scopus subject areas

- Mathematics(all)
- Education