Question 148
For which positive integers $n \ge 2$ do there exist $n$ odd (not necessarily different) numbers $a_1, a_2, \dots, a_n$ such that
$a_1^2 + a_2^2 + \dots + a_n^2$ is the square of some positive integer?
$a_1^2 + a_2^2 + \dots + a_n^2$ is the square of some positive integer?