Geodesic
On the spacing between terms of generalized Fibonacci sequences
Diego Marques 1
1 Mathematics Department University of Brasilia Brasilia, Brazil
Colloquium Mathematicum, Tome 134 (2014) no. 2, pp. 267-280 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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For $k\geq 2$, the $k$-generalized Fibonacci sequence $(F_n^{(k)})_{n}$ is defined to have the initial $k$ terms $0,0,\ldots ,0,1$ 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 $F_m^{(k)}-F_n^{(\ell )}=c>0$ (under some weak assumptions) is bounded by an effectively computable constant depending only on $c$.
DOI : 10.4064/cm134-2-10
Keywords: geq k generalized fibonacci sequence defined have initial terms ldots each term afterwards sum preceding terms prove number solutions diophantine equation f ell under weak assumptions bounded effectively computable constant depending only nbsp

Diego Marques  1

1 Mathematics Department University of Brasilia Brasilia, Brazil 
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Diego Marques. On the spacing between terms of generalized Fibonacci sequences. Colloquium Mathematicum, Tome 134 (2014) no. 2, pp. 267-280. doi: 10.4064/cm134-2-10

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