Dec. 1986: C.B. Lacampagne and J.L. Selfridge: Pairs of Squares with Consecutive Digits (Math. Mag. Vol. 59, no. 5: 270 – 275) www.jstor.org/stable/2689401) contains a list of pairs of square numbers whose difference is a repunit.
Their springboard was a grade-school exercise raised by Mary Grace Kantowski to find all 2-digit and 3-digit numbers whose squares are such that subtracting 1 from every number you get another square number.
Lacampagne and Selfridge expanded the question to search for the list of all pairs of square numbers $x^2$ and $y^2$ such that $x^2 - y^2$ is a repunit (omitting all pairs such that $x^2$ contains zeroes).
They attacked the problem by factorising the repunit $R_n$ for each $n$ into $a$ and $b$ and using $x^2 + y^2 = (x + y) (x - y)$ and setting $x + y = a$, $x - y = b$. A simple way to generate all such pairs.
But it seems they completely forgot to take $a = R_n$ and $b = 1$. Thus they missed the simple instance $56^2 - 55^2 = 111$.
Similarly they missed all numbers of a similar pattern: $556^2 - 555^2 = 1111, 5556^2 - 5555^2 = 11111$, and so on.
Have I missed something from their dissertation, that is, was this a deliberate omission? (I would gather not, otherwise they would not have listed $6^2 - 5^2 = 11$), and if not, has this been commented on before now? I have done some research (i.e. "googled around a bit") and have not found anything.