Question 79
Determine the smallest integer $n \geqslant 2$ for which positive integers $a_{1}, \ldots, a_{n}$ exist with
$$
a_{1}^{2}+\ldots+a_{n}^{2} \mid \left(a_{1}+\ldots+a_{n}\right)^{2}-1
$$
$$
a_{1}^{2}+\ldots+a_{n}^{2} \mid \left(a_{1}+\ldots+a_{n}\right)^{2}-1
$$