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ON $k$-GENERALIZED PADOVAN NUMBERS WHICH ARE REPDIGITS IN BASE $\eta$
Keywords:
Diophantine equations, linear forms in logarithms, k-Padovan numbers, repdigit, reduction methodDOI:
https://doi.org/10.17654/0972555525021Abstract
Let $k \geq 3$. Then the $k$-Padovan sequence is a generalization of the Padovan sequence. The sequence's first $k$ terms are $0,0, \ldots, 0,1,1$. This paper identifies all repdigits that can be expressed as $k$-Padovan numbers in base $\eta$, where $2 \leq \eta \leq 10$, through the application of the theory of linear forms in logarithms of algebraic numbers and a modified version of the Baker-Davenport reduction method.
Received: January 27, 2025
Accepted: May 9, 2025
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