### Abstract

Continuing the recent work of the second author, we prove that the diophantine equation fα (x, y) = x^{4} - αx^{3}y - x^{2}y^{2} + αxy^{3} + y^{4} = 1 for /α/ ≥ 3 has exactly 12 solutions except when |α| = 4. when it has 16 solutions. If α = α(α) denotes one of the zeros of f_{α}(xx, 1), then for lαl ≥ 4 we also find all γ ∈ ℤ[α] with ℤ[γ] = ℤ[α].

Original language | English |
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Pages (from-to) | 341-354 |

Number of pages | 14 |

Journal | Mathematics of Computation |

Volume | 65 |

Issue number | 213 |

DOIs | |

Publication status | Published - Jan 1 1996 |

### Keywords

- Distributed computation
- Index form equation
- Linear forms in the logarithms of algebraic numbers
- Thue equation

### ASJC Scopus subject areas

- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics

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## Cite this

Mignotte, M., Pethö, A., & Roth, R. (1996). Complete solutions of a family of quartic Thue and index form equations.

*Mathematics of Computation*,*65*(213), 341-354. https://doi.org/10.1090/S0025-5718-96-00662-X