On Homogeneous Combinations of Linear Recurrence Sequences

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18440%2F20%3A50017567" target="_blank" >RIV/62690094:18440/20:50017567 - isvavai.cz</a>
Alternative codes found
RIV/62690094:18470/20:50017567
Result on the web
<a href="https://www.mdpi.com/2227-7390/8/12/2152" target="_blank" >https://www.mdpi.com/2227-7390/8/12/2152</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/math8122152" target="_blank" >10.3390/math8122152</a>

Result language
angličtina
Original language name
On Homogeneous Combinations of Linear Recurrence Sequences
Original language description
Let (F-n)(n >= 0) be the Fibonacci sequence given by Fn+2 = Fn+1 + F-n, for n >= 0, where F-0 = 0 and F-1 = 1. There are several interesting identities involving this sequence such as F-n(2) + F-n+1(2) = F2n+1, for all n >= 0. In 2012, Chaves, Marques and Togbe proved that if (Gm)m is a linear recurrence sequence (under weak assumptions) and G(n+1)(s) vertical bar center dot center dot center dot vertical bar G(n+l)(s)is an element of(G(m))(m), for infinitely many positive integers n, then s is bounded by an effectively computable constant depending only on l and the parameters of (G(m))(m). In this paper, we shall prove that if P(x(1), ..., x(l)) is an integer homogeneous s-degree polynomial (under weak hypotheses) and if P(G(n+1), ...,G(n+l)) is an element of(G(m))(m) for infinitely many positive integers n, then s is bounded by an effectively computable constant depending only on l, the parameters of (G(m))(m) and the coefficients of P.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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