Talk:Repdigit Triangular Numbers

Sorry for this lousy, fragmented proof.

This is modified from https://sdaos.org/wp-content/uploads/pdfs/Vol%2051%201972/72p52.pdf.

However I am 90% confident this proof is flawed, when I was halfway through rewriting it.

For anyone who stumbled across this somehow, the main flaw of the linked proof is that no zeroes are considered to be part of the "chains" that generate squares that end repdigit-like.

There is also the problem of some chains can still be extended, probably infinitely (e.g. 9-7-9-7-1-4-1-1-9-4-...), contrary to the claims of the authors, but that is comparatively minor.

--RandomUndergrad (talk) 12:32, 11 March 2022 (UTC)

The same authors published a proof in J.R.Math Vol. 8, which I have no access to at the moment.

Neither do I have access to Bir Kafle et al., Triangular repblocks, Fib. Q., 56:4 (2018), 325-328. --RandomUndergrad (talk) 12:45, 17 July 2020 (UTC)

I'm not sure how much help the above citation is going to be, because according to the abstract, it only covers $55$ and $66$ and not $666$. I'm toying with the idea of subscribing to FQ at the moment. --prime mover (talk) 13:02, 17 July 2020 (UTC)