Repdigits as difference of two balancing or Lucas-balancing numbers

Repdigits are natural numbers formed by the repetition of a single digit. In this paper, we study the problem of writing repdigits as the difference of two balancing or Lucas-balancing numbers. The method of proof involves the application of Baker’s theory for linear forms in logarithms of algebraic numbers and the Baker-Davenport reduction procedure. Computations are done with the help of a simple computer program in {\it Mathematica}.