Find digits
![x, y, z](/media/m/e/1/6/e160f3439547ca8c1afcc35a1c26f080.png)
such that the equality
![\sqrt{\underbrace{\overline{xx\cdots x}}_{n \text{ times}}-\underbrace{\overline{yy\cdots y}}_{n \text{ times}}}=\underbrace{\overline{zz\cdots z}}_{n \text{ times}}](/media/m/8/4/7/84791c301fe14ce5f92a595c1405d9a8.png)
holds for at least two values of
![n \in \mathbb N](/media/m/4/e/6/4e671e4759f4315f56d66487a7496230.png)
, and in that case find all
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
for which this equality is true.
%V0
Find digits $x, y, z$ such that the equality $$\sqrt{\underbrace{\overline{xx\cdots x}}_{n \text{ times}}-\underbrace{\overline{yy\cdots y}}_{n \text{ times}}}=\underbrace{\overline{zz\cdots z}}_{n \text{ times}}$$ holds for at least two values of $n \in \mathbb N$, and in that case find all $n$ for which this equality is true.