### Abstract

We explicitly solve the equation Ax^{n}-By^{n} = ±1 and, along the way, we obtain new results for a collection of equations Ax^{n}-By^{n} = z^{m} with m ∈ {3, n}, where x, y, z, A, B, and n are unknown nonzero integers such that n ≤ 3, AB = p^{α}q^{β} with nonnegative integers α and β and with primes 2 ≤ p < q < 30. The proofs require a combination of several powerful methods, including the modular approach, recent lower bounds for linear forms in logarithms, somewhat involved local considerations, and computational techniques for solving Thue equations of low degree.

Original language | English |
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Pages (from-to) | 61-77 |

Number of pages | 17 |

Journal | Fundamental and Applied Mathematics |

Volume | 16 |

Issue number | 5 |

Publication status | Published - Dec 1 2010 |

### ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory
- Geometry and Topology
- Applied Mathematics

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## Cite this

Gyory, K., & Pintér, A. (2010). Binomial Thue equations, ternary equations, and power values of polynomials.

*Fundamental and Applied Mathematics*,*16*(5), 61-77.