Address: Departamento de Matemáticas, Universidad del Cauca, Calle 5 No 4–70, Popayán, Colombia
E-mail:
jbravo@unicauca.edu.co
joseherrera@unicauca.edu.co
Abstract: 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 $(P_n^{(2)})_n$.
AMSclassification: primary 11B39; secondary 11J86.
Keywords: generalized Pell numbers, repdigits, linear forms in logarithms, reduction method.
DOI: 10.5817/AM2020-4-249