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# Article

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Keywords:
generalized Pell numbers; repdigits; linear forms in logarithms; reduction method
Summary:
For an integer \$k\ge 2\$, let \$({n})_n\$ be the \$k-\$generalized Pell sequence which starts with \$0,\ldots ,0,1\$ (\$k\$ terms) and each term afterwards is given by the linear recurrence \${n} = 2{n-1}+{n-2}+\cdots +{n-k}\$. In this paper, we find all \$k\$-generalized Pell numbers with only one distinct digit (the so-called repdigits). Some interesting estimations involving generalized Pell numbers, that we believe are of independent interest, are also deduced. This paper continues a previous work that searched for repdigits in the usual Pell sequence \$(P_n^{(2)})_n\$.
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