On the spacing between terms of generalized Fibonacci sequences

Diego Marques

Diego Marques

Colloquium Mathematicae, Tome 135 (2014), p. 267-280 / Harvested from The Polish Digital Mathematics Library

Résumé

For k ≥ 2, the k-generalized Fibonacci sequence $(F ₙ^{(k)}) ₙ$ 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 $F ₘ^{(k)} - F ₙ^{(ℓ)} = c > 0$ (under some weak assumptions) is bounded by an effectively computable constant depending only on c.

Publié le : 2014-01-01

Zbl 06285564

EUDML-ID : urn:eudml:doc:286363

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     title = {On the spacing between terms of generalized Fibonacci sequences},
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     volume = {135},
     year = {2014},
     pages = {267-280},
     zbl = {06285564},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm134-2-10}
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Diego Marques. On the spacing between terms of generalized Fibonacci sequences. Colloquium Mathematicae, Tome 135 (2014) pp. 267-280. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm134-2-10/