[Submitted on 13 Jun 2026]

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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 $P_4 = 12 = 1\|2$.

Submission history

From: Faye Bernadette [view email]
[v1] Sat, 13 Jun 2026 13:04:36 UTC (16 KB)

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