### Abstract

We study some fine arithmetic properties of the components of solutions of a decomposable form equation. Lower growth rates for the greatest prime factor of a component are obtained for density 1 of the solutions. Also, high pure powers are shown to occur rarely. Computations illustrate the applicability of our results; for example, to the study of units in abelian group rings.

Original language | English |
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Pages (from-to) | 27-40 |

Number of pages | 14 |

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

Volume | 139 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jul 2005 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**On some arithmetical properties of solutions of decomposable form equations.** / Everest, Graham; Györy, K.

Research output: Contribution to journal › Article

*Mathematical Proceedings of the Cambridge Philosophical Society*, vol. 139, no. 1, pp. 27-40. https://doi.org/10.1017/S0305004104008230

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TY - JOUR

T1 - On some arithmetical properties of solutions of decomposable form equations

AU - Everest, Graham

AU - Györy, K.

PY - 2005/7

Y1 - 2005/7

N2 - We study some fine arithmetic properties of the components of solutions of a decomposable form equation. Lower growth rates for the greatest prime factor of a component are obtained for density 1 of the solutions. Also, high pure powers are shown to occur rarely. Computations illustrate the applicability of our results; for example, to the study of units in abelian group rings.

AB - We study some fine arithmetic properties of the components of solutions of a decomposable form equation. Lower growth rates for the greatest prime factor of a component are obtained for density 1 of the solutions. Also, high pure powers are shown to occur rarely. Computations illustrate the applicability of our results; for example, to the study of units in abelian group rings.

UR - http://www.scopus.com/inward/record.url?scp=22544462833&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22544462833&partnerID=8YFLogxK

U2 - 10.1017/S0305004104008230

DO - 10.1017/S0305004104008230

M3 - Article

AN - SCOPUS:22544462833

VL - 139

SP - 27

EP - 40

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 1

ER -