# If $R$ is such that any number with a single repeated number as its digit is present in $R$, then find all even $n, T(n) \in R$

Let $R$ denote the set of positive integers whose base ten expression is a single repeated digit(Examples: $11,3,444$). Let $T(n) = (n-2)^2 + n^2 + (n+2)^2$ where n is a non-negative integer. Find all even integers n such that $T(n) \in R$

My attempt: Its too long to type so I have provided an image This leaves me hanging at a square of the form $2960, 2962960, 2962962960,....$ which essentially means there are no solutions. I must have gone wrong somewhere, it would be really appreciated if anyone could point out where.

• A number ending in $0$ can be a square only if it ends with two zeros. – egreg Jun 27 '18 at 15:01

There is $n=0$ Otherwise, if $n^2$ ends in $0$, then it ends in $00$. I agree with your solution.