Triangular Numbers With a Single Repeated Digit
Number Theory
2025-06-03 v2
Abstract
The question of which triangular numbers have a decimal representation containing a single repeated digit seamed to be settled since at least the 1970s: Ballew and Weger provided a complete list and a proof that these are the only numbers of this kind. This assertion is referenced by other authors in the field. However, their proof is flawed. We present a new and elementary proof of the statement, which corrects the error.
Cite
@article{arxiv.2407.21487,
title = {Triangular Numbers With a Single Repeated Digit},
author = {Christian Hercher and Karl Fegert},
journal= {arXiv preprint arXiv:2407.21487},
year = {2025}
}