On the spacing between terms of generalized Fibonacci sequences

• Autorzy: Diego Marques
• Języki publikacji: EN

Abstrakty

EN

For k ≥ 2, the k-generalized Fibonacci sequence $(Fₙ^{(k)})ₙ$ is defined to have the initial k terms 0,0,...,0,1 and be such that each term afterwards is the sum of the k preceding terms. We will prove that the number of solutions of the Diophantine equation $Fₘ^{(k)} - Fₙ^{(ℓ)} = c > 0$ (under some weak assumptions) is bounded by an effectively computable constant depending only on c.

Kategorie tematyczne

• 11B39: Fibonacci and Lucas numbers and polynomials and generalizations
• 11J86: Linear forms in logarithms; Baker's method

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2014
• Tom: 134
• Numer: 2
• Strony: 267-280

Daty

wydano

2014

Twórcy

autor

Diego Marques

• Mathematics Department, University of Brasilia, Brasilia, Brazil

Identyfikatory

DOI

10.4064/cm134-2-10