2013 IMO Shortlist N4

Determine whether there exists an infinite sequence of nonzero digits $a_{1}, a_{2}, a_{3}, \ldots$ and a positive integer $N$ such that for every integer $k>N$, the number $\overline{a_{k} a_{k-1} \ldots a_{1}}$ is a perfect square. (Iran)

确定是否存在非零数字 $a_{1}、a_{2}、a_{3}、\ldots$ 和正整数 $N$ 的无限序列，使得对于每个整数 $k>N$，数字 $\overline{a_{k} a_{k-1} \ldots a_{1}}$ 是完全平方数。 (伊朗)