## Abstract

The number of solutions of the Diophantine equation ( _{m} ^{x}) + β( _{n} ^{y}) = γ with α, β, γ ∈ ℚ and m, n ∈ ℕ, m ≥ n in rational integers (x, y) is investigated. We apply the general BILU-TICHY-criterion [5] for polynomial Diophantine equations f(x) = g(y) in order to obtain ineffective finiteness of solutions (x, y) in the case m, n ≥ 3. Simplicity and two-interval-monotonicity of the local extrema of ( _{m} ^{x}) also guarantee finiteness in the case min(m, n) = 2.

Original language | English |
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Pages (from-to) | 155-165 |

Number of pages | 11 |

Journal | Publicationes Mathematicae |

Volume | 64 |

Issue number | 1-2 |

Publication status | Published - 22 Mar 2004 |

## Keywords

- Binomial coefficients
- Diophantine equations
- Finiteness results

## ASJC Scopus subject areas

- Mathematics(all)

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