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On Y-coordinates of Pell equations which are Lucas numbers
Journal article   Peer reviewed

On Y-coordinates of Pell equations which are Lucas numbers

Bilizimbeye Edjeou, Bernadette Faye, Carlos A. Gomez and Florian Luca
The Ramanujan journal, Vol.59(4), pp.1091-1136
01/12/2022
DOI: https://doi.org/10.1007/s11139-022-00613-0

Abstract

Mathematics Physical Sciences Science & Technology
Let d >= 2 be an integer which is not a square. We show that if (L-n)(n >= 0) is the Lucas sequence and (X-m, Y-m)(m >= 1) is the mth solution of the Pell equation X-2 - dY(2) = +/- 1, then the equation Y-m = L-n has at most two positive integer solutions (m, n) except for d = 2 when it has the three solutions (m, n) = (1, 1), (2, 0), (5, 7).

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