Turkish Journal of Mathematics
DOI
10.3906/mat-1808-2
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
First Page
207
Last Page
223
Recommended Citation
RIHANE, SALAH EDDINE; HERNANE, MOHAND OUAMAR; and TOGBE, ALAIN
(2019)
"The $X$-coordinates of Pell equations and Padovan numbers,"
Turkish Journal of Mathematics: Vol. 43:
No.
1, Article 17.
https://doi.org/10.3906/mat-1808-2
Available at:
https://journals.tubitak.gov.tr/math/vol43/iss1/17
