Thabit and Williams Numbers Base $b$ as a Sum or Difference of Two $g$-Repdigits

Abstract

We investigate cases where Thabit and Williams numbers in base $b$ can be expressed as the sum or difference of two $g$-repdigits. For specific values of $b$ and $g$, we describe parametric solutions yielding infinitely many solutions for some equations and establish upper bounds for the parameters of the remaining finitely many solutions. As an illustration, we also provide a complete solution for some equations.

arXiv comment32 pages, some mistakes corrected, Proposition 1 has more cases