Observe that \(14\) isn’t a square
number but \(144=12^2\) and \(1444=38^2\) are both square numbers. Let
\(k_1^2=\overline{a_n...a_1a_0}\) the
decimal representation of a square number.
Is it possible that \(\overline{a_n...a_1a_0a_0}\) and \(\overline{a_n...a_1a_0a_0a_0}\) are also
both square numbers?