Question 125
Let $n$ be an integer greater than $3$, and let $a_1, a_2, \dots, a_n$ be nonnegative real numbers with $a_1 + a_2 + \dots + a_n = 2$.
Determine the minimum value of
$$
\frac{a_1}{a_2^2+1} + \frac{a_2}{a_3^2+1} + \cdots + \frac{a_n}{a_1^2+1}.
$$
Determine the minimum value of
$$
\frac{a_1}{a_2^2+1} + \frac{a_2}{a_3^2+1} + \cdots + \frac{a_n}{a_1^2+1}.
$$