Does there exist a positive integer \(n\) and digits \( a_1 \neq 0, a_2, \ldots, a_n \) such that

\[ \sqrt{ \overline{a_1 a_2 \ldots a_{n-1} a_n }} - \sqrt{ \overline{a_1 a_2\ldots a_{n-1} } } = a_n ? \]

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