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arXiv · 2407.21487

Triangular Numbers With a Single Repeated Digit

Christian Hercher·Karl Fegert
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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.

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Christian Hercher, Karl Fegert. 2024-11-04. Triangular Numbers With a Single Repeated Digit. https://arxiv.org/abs/2407.21487

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