Question 91
Assume that $n$ is a given positive integer. Find all of the integer groups $(a_1, a_2, \dots, a_n)$ satisfying the conditions:
(1) $a_1 + a_2 + \dots + a_n \ge n^2$;
(2) $a_1^2 + a_2^2 + \dots + a_n^2 \le n^3 + 1$.
(1) $a_1 + a_2 + \dots + a_n \ge n^2$;
(2) $a_1^2 + a_2^2 + \dots + a_n^2 \le n^3 + 1$.