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.

DOI

10.3906/mat-1808-2

Keywords

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

First Page

207

Last Page

223

Recommended Citation

RIHANE, S. E, HERNANE, M. O, & TOGBE, A (2019). The $X$-coordinates of Pell equations and Padovan numbers. Turkish Journal of Mathematics 43 (1): 207-223. https://doi.org/10.3906/mat-1808-2

Download