On some combinations of terms of a recurrence sequence

Pavel Trojovský

Chaos, Solitons & Fractals, 2016, vol. 82, issue C, 34-37

Abstract: Let (Gm)m ≥ 0 be an integer linear recurrence sequence (under some weak technical conditions) and let x ≥ 1 be an integer. In this paper, we are interested in the problem of finding combinations of the form xGn+Gn−1 which belongs to (Gm)m ≥ 0 for infinitely many positive integers n. In this case, we shall make explicit an upper bound for x which only depends on the roots of the characteristic polynomial of this recurrence. As application, we shall study the k-nacci case.

Keywords: Combinations; Recurrence sequence (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:82:y:2016:i:c:p:34-37

DOI: 10.1016/j.chaos.2015.10.033

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