Let $s(n)$ denote the sum of the squares of the digits of $n$. For example, $s(14) = 1 ^ 2 + 4 ^ 2 = 17$ Determine all integers adding n for which $s(n) = n$ holds.
I bound it to $243$ due to $9^2 *4 < 1000$. And thus $n$ must have at most $3$ digits so $3*81 =243$. I have no idea what to do now.