Bernadette Faye, Florian Luca
Published 2016-05-12Version 1
Let $b\ge 2$ be a given integer. In this paper, we show that there only finitely many positive integers $d$ which are not squares, such that the Pell equation $X^2-dY^2=1$ has two positive integer solutions $(X,Y)$ with the property that their $X$-coordinates are base $b$-repdigits. We also give an upper bound on the largest such $d$ in terms of $b$.
Comments: All comments are welcome!
Sums of S-units in X-coordinates of Pell equations
Positive Integer Solutions of the Pell Equation $x^{2}-dy^{2}=N,$ $% d\in \left\{k^{2}\pm 4,\text{}k^{2}\pm 1\right\} $ and $N\in \left\{\pm 1,\pm 4\right\}
On the $X$-coordinates of Pell equations which are Tribonacci numbers
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