X-coordinates of Pell equations which are Lucas numbers

X-coordinates of Pell equations which are Lucas numbers

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 = ± 1 which is a Lucas number, with a few exceptions that we completely characterize.

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Veröffentlicht in:Boletín de la Sociedad Matemática Mexicana 2019-11, Vol.25 (3), p.481-493
Hauptverfasser: Kafle, Bir, Luca, Florian, Togbé, Alain
Format: Artikel
Sprache:eng
Schlagworte:
Integers
Mathematics
Mathematics and Statistics
Numbers
Original Article
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Beschreibung
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 = ± 1 which is a Lucas number, with a few exceptions that we completely characterize.
ISSN:1405-213X
2296-4495
DOI:10.1007/s40590-018-0221-y