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arXiv · 2509.04503

Solving Skolem problem for negative indexed $k-$generalized Pell numbers

Monalisa Mohapatra·Pritam Kumar Bhoi·Gopal Krishna Panda
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Abstract

In this paper, we address the Skolem problem for the $k$-generalized Pell sequence $(P_n^{(k)})_{n\geq2-k}$ extended to negative indices. We focus on identifying and bounding the indices $n<0$ for which $P_n^{(k)}=0.$ In particular, we establish that the zero multiplicity of $P_n^{(k)}$ is $ \chi_k = \lfloor k^2/4\rfloor$ for all $k \in [4, 500].$

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Monalisa Mohapatra, Pritam Kumar Bhoi, Gopal Krishna Panda. 2025-09-02. Solving Skolem problem for negative indexed $k-$generalized Pell numbers. https://arxiv.org/abs/2509.04503

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