x-Coordinates of Pell equations which are Tribonacci numbers II

x-Coordinates of Pell equations which are Tribonacci numbers II

For an integer d ≥ 2 which is not a square, we show that there is at most one value of the positive integer x participating in the Pell equation x 2 - d y 2 = ± 4 which is a Tribonacci number, with a few exceptions that we completely characterize.

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Veröffentlicht in:Periodica mathematica Hungarica 2019-12, Vol.79 (2), p.157-167
Hauptverfasser: Kafle, Bir, Luca, Florian, Togbé, Alain
Format: Artikel
Sprache:eng
Schlagworte:
Integers
Mathematics
Mathematics and Statistics
Numbers
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Zusammenfassung:For an integer d ≥ 2 which is not a square, we show that there is at most one value of the positive integer x participating in the Pell equation x 2 - d y 2 = ± 4 which is a Tribonacci number, with a few exceptions that we completely characterize.
ISSN:0031-5303
1588-2829
DOI:10.1007/s10998-018-0264-x