Question 142
Prove that there exist an integer $m \ge 2002$ and $m$ distinct positive integers $a_1, a_2, \dots, a_m$ such that the number
$$
\prod_{i=1}^{m} a_i^2 - 4 \sum_{i=1}^{m} a_i^2
$$
is a perfect square.
$$
\prod_{i=1}^{m} a_i^2 - 4 \sum_{i=1}^{m} a_i^2
$$
is a perfect square.