- Turkish Journal of Mathematics
- Vol: 43 Issue: 1
- The $X$-coordinates of Pell equations and Padovan numbers
The $X$-coordinates of Pell equations and Padovan numbers
Authors : Salah Eddine Rihane, Mohand Ouamar Hernane, Alain Togbe
Pages : 207-223
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Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :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