On the divisibility F-k vertical bar F-x(2) + F-x+1

On the divisibility F-k vertical bar F-x(2) + F-x+1

Let F-n and L-n be the nth Fibonacci and Lucas numbers, respectively. We show that if F-k vertical bar F-x(2) + F-x + 1, then k is an element of{4,7}; if L-k vertical bar F-x(2) + F-x + 1, then k is an element of {2, 4}.

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Veröffentlicht in:ScienceAsia : journal of the Science Society of Thailand 2021-02, Vol.47 (1), p.106-110
Hauptverfasser: Luca, Florian, Pongsriiam, Prapanpong, Szalay, Laszlo
Format: Artikel
Sprache:eng
Schlagworte:
Multidisciplinary Sciences
Science & Technology
Science & Technology - Other Topics
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Zusammenfassung:Let F-n and L-n be the nth Fibonacci and Lucas numbers, respectively. We show that if F-k vertical bar F-x(2) + F-x + 1, then k is an element of{4,7}; if L-k vertical bar F-x(2) + F-x + 1, then k is an element of {2, 4}.
ISSN:1513-1874
DOI:10.2306/scienceasia1513-1874.2021.005