Salah Eddine RIHANE, Mohand Ouamar HERNANE, Alain TOGBE

The $X$-coordinates of Pell equations and Padovan numbers

In this paper, we show that there is at most one value of the positive integer $X$ participating in the Pell equation $X^2-dY^2=k$, where $k\in\{\pm1,\pm4\}$, which is a Padovan number, with a few exceptions that we completely characterize.

Keywords:

Padovan numbers Pell equation, Linear form in logarithms, reduction method,

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ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

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