The Diophantine equation α( m x) + β( n y) = γ

Th Stoll*, R. F. Tichy

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)155-165
Number of pages11
JournalPublicationes Mathematicae
Issue number1-2
Publication statusPublished - 22 Mar 2004


  • Binomial coefficients
  • Diophantine equations
  • Finiteness results

ASJC Scopus subject areas

  • Mathematics(all)


Dive into the research topics of 'The Diophantine equation α( m x) + β( n y) = γ'. Together they form a unique fingerprint.

Cite this