Balancing numbers which are concatenations of three repdigits

F. Erduvan; R. Keskin

doi:10.15330/cmp.16.1.148-157

Balancing numbers which are concatenations of three repdigits

Authors

F. Erduvan Sakarya University, 54050, Serdivan, Sakarya, Turkey https://orcid.org/0000-0001-7254-2296
R. Keskin Sakarya University, 54050, Serdivan, Sakarya, Turkey https://orcid.org/0000-0003-2547-2082

https://doi.org/10.15330/cmp.16.1.148-157

Keywords:

balancing number, concatenation, repdigit, Diophantine equation, linear form in logarithms

Published online: 2024-06-06

Abstract

In this study, it is shown that the only balancing numbers which are concatenations of three repdigits are $204$ and $1189$. The proof depends on lower bounds for linear forms and some tools from Diophantine approximation.