Question 149
Let $R^+$ denote the set of all positive real numbers. Given an integer $n \ge 3$, find all functions $f: R^+ \to R^+$ such that for any $n$ positive real numbers $a_1, \cdots, a_n$,
$$
\sum_{i=1}^{n} (a_i - a_{i+1}) f(a_i + a_{i+1}) = 0,
$$
where $a_{n+1} = a_1$.
$$
\sum_{i=1}^{n} (a_i - a_{i+1}) f(a_i + a_{i+1}) = 0,
$$
where $a_{n+1} = a_1$.