Repdigit triangular numbers

216 Views Asked by At

Problem

Find all the triangular numbers that, written in base $10$, has all their digits the same.

My work so far:

I know that the solutions are $0$, $1$, $3$, $6$, $55$, $66$ and $666$.

My work on the problem is here.

I also know that the proof that there aren't any more solutions is an article of Journal of recreational mathematics, volume 8 by Ballew and Weger, p. 96. The title is precisely Repdigit triangular numbers.

But I don't have access to this article, not even paying for it. As far as I know, it has not been scanned, and my local library has not it.

I'm very interested in that proof (or any proof).

Thanks.