### Abstract

Let G_{n} be a second order linear recursive sequence, which satisfy certain conditions, and p be a prime. In this paper we describe an algorithm with which one can compute all but possible one integer solutions n,z of the diophantine equation G_{n}=p^{z}. In the exceptional case the algorithm gives an n such that G_{n} is the only possible further power of p. We give an upper bound for the running time too.

Original language | English |
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Title of host publication | EUROCAL 1985 - European Conference on Computer Algebra, Proceedings |

Publisher | Springer Verlag |

Pages | 503-512 |

Number of pages | 10 |

ISBN (Print) | 9783540159841 |

DOIs | |

Publication status | Published - Jan 1 1985 |

Event | European Conference on Computer Algebra, EUROCAL 1985 - Linz, Austria Duration: Apr 1 1985 → Apr 3 1985 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 204 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | European Conference on Computer Algebra, EUROCAL 1985 |
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Country | Austria |

City | Linz |

Period | 4/1/85 → 4/3/85 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

_{n}=p

^{z}In

*EUROCAL 1985 - European Conference on Computer Algebra, Proceedings*(pp. 503-512). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 204 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-15984-3_320

**On the solution of the diophantine equation G _{n}=p^{z} .** / Pethő, A.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

_{n}=p

^{z}in

*EUROCAL 1985 - European Conference on Computer Algebra, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 204 LNCS, Springer Verlag, pp. 503-512, European Conference on Computer Algebra, EUROCAL 1985, Linz, Austria, 4/1/85. https://doi.org/10.1007/3-540-15984-3_320

_{n}=p

^{z}In EUROCAL 1985 - European Conference on Computer Algebra, Proceedings. Springer Verlag. 1985. p. 503-512. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-15984-3_320

}

TY - GEN

T1 - On the solution of the diophantine equation Gn=pz

AU - Pethő, A.

PY - 1985/1/1

Y1 - 1985/1/1

N2 - Let Gn be a second order linear recursive sequence, which satisfy certain conditions, and p be a prime. In this paper we describe an algorithm with which one can compute all but possible one integer solutions n,z of the diophantine equation Gn=pz. In the exceptional case the algorithm gives an n such that Gn is the only possible further power of p. We give an upper bound for the running time too.

AB - Let Gn be a second order linear recursive sequence, which satisfy certain conditions, and p be a prime. In this paper we describe an algorithm with which one can compute all but possible one integer solutions n,z of the diophantine equation Gn=pz. In the exceptional case the algorithm gives an n such that Gn is the only possible further power of p. We give an upper bound for the running time too.

UR - http://www.scopus.com/inward/record.url?scp=0042340465&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042340465&partnerID=8YFLogxK

U2 - 10.1007/3-540-15984-3_320

DO - 10.1007/3-540-15984-3_320

M3 - Conference contribution

AN - SCOPUS:0042340465

SN - 9783540159841

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 503

EP - 512

BT - EUROCAL 1985 - European Conference on Computer Algebra, Proceedings

PB - Springer Verlag

ER -