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arXiv · 2606.15290

On concatenations of two $k$-generalized Pell numbers

Cherif B. Deme·Kancou D. Fall·Khady Faye·Bernadette Faye
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Abstract

We study the concatenation of two $k$-generalized Pell numbers. More precisely, we determine all solutions of the equation $P_n^{(k)} = P_m^{(k)} \cdot 10^{d} + P_p^{(k)}$, where $d$ is the number of decimal digits of $P_p^{(k)}$. We prove that for $k \ge 3$ there are no solutions, while for $k = 2$ the only solution is $P_4 = 12 = 1\|2$.

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Cherif B. Deme, Kancou D. Fall, Khady Faye, Bernadette Faye. 2026-06-13. On concatenations of two $k$-generalized Pell numbers. https://arxiv.org/abs/2606.15290

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