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- W4313012335 abstract "Let $kgeq 2$ be an integer and let $(P_{n}^{(k)})_{ngeq 2-k}$ be the $k$ -generalized Pell sequence defined by begin{equation*} P_{n}^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+...+P_{n-k}^{(k)} end{equation*} for $ngeq 2$ with initial conditions begin{equation*} P_{-(k-2)}^{(k)}=P_{-(k-3)}^{(k)}=cdot cdot cdot =P_{-1}^{(k)}=P_{0}^{(k)}=0,P_{1}^{(k)}=1. end{equation*} In this study, we deal with the Diophantine equation begin{equation*} P_{n}^{(k)}=dleft( frac{b^{m}-1}{b-1}right) end{equation*} in positive integers $n,m,k,b,d$ such that $mgeq 2,$ $2leq bleq 9$ and $ 1leq dleq b-1$. We show that the repdigits in the base $b$ in the $k-$ generalized Pell sequence, which have at least two digits, are the numbers begin{eqnarray*} P_{7}^{(4)} &=&228=(444)_{7},text{ }P_{4}^{(2)}=12=(22)_{5}text{, }% P_{6}^{(2)}=70=(77)_{9}text{;} P_{4}^{(k)} &=&13=(111)_{3}text{ } end{eqnarray*} for $kgeq 3$ and begin{equation*} P_{3}^{(k)}=5=(11)_{4} end{equation*} for $kgeq 2.$" @default.
- W4313012335 created "2023-01-05" @default.
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- W4313012335 date "2022-01-01" @default.
- W4313012335 modified "2023-10-18" @default.
- W4313012335 title "$k$-generalized Pell numbers which are repdigits in base $b$" @default.
- W4313012335 doi "https://doi.org/10.55730/1300-0098.3321" @default.
- W4313012335 hasPublicationYear "2022" @default.
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