On the spacing between terms of generalized Fibonacci sequences

Diego Marques. "On the spacing between terms of generalized Fibonacci sequences." Colloquium Mathematicae 134.2 (2014): 267-280. <http://eudml.org/doc/286363>.

@article{DiegoMarques2014,
abstract = {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.},
author = {Diego Marques},
journal = {Colloquium Mathematicae},
keywords = {-generalized Fibonacci numbers; linear forms in logarithms; Pillai's equation; spacing; reduction method},
language = {eng},
number = {2},
pages = {267-280},
title = {On the spacing between terms of generalized Fibonacci sequences},
url = {http://eudml.org/doc/286363},
volume = {134},
year = {2014},
}

TY - JOUR
AU - Diego Marques
TI - On the spacing between terms of generalized Fibonacci sequences
JO - Colloquium Mathematicae
PY - 2014
VL - 134
IS - 2
SP - 267
EP - 280
AB - 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.
LA - eng
KW - -generalized Fibonacci numbers; linear forms in logarithms; Pillai's equation; spacing; reduction method
UR - http://eudml.org/doc/286363
ER -