Question 128
Consider a positive integer $n$ and the set $A_n = \{1, 3, 5, \dots, 2n - 1\}$. For each pair $(a, b)$, where $a, b \in A_n$ we construct the concatenated number $m = \overline{ab}$, obtained by joining the numbers $a$ and $b$. For instance, for $19, 37 \in A_{30}$, the concatenated number is $m = 1937$.
a) What is the smallest number $n \in \mathbb{N}^*$ for which we get at least a perfect square?
b) Find the largest perfect square that can be obtained for $n = 50$.
a) What is the smallest number $n \in \mathbb{N}^*$ for which we get at least a perfect square?
b) Find the largest perfect square that can be obtained for $n = 50$.