Let $k\geq 2$. A generalization of the well-known Pell sequence is the $k$-Pell sequence whose first $k$ terms are $0,\ldots,0,1$ and each term afterwards is given by the linear recurrence $$P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots +P_{n-k}^{(k)}.$$
The goal of this talk is to show that $11, 33, 55, 88$ and $99$ are only repdigits expressible as sum or difference of two $k$-Pell numbers. The proof of this main theorem uses lower bounds for linear forms in logarithms of algebraic numbers (Baker's method) and a modified version of Baker-Davenport reduction method (due to Dujella and Pethö). Our result extends that of Bravo and Herrera.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/node/246