Question 18
Find all functions $f: \mathbb{R} \to \mathbb{R}$ satisfying
$$
(a-b)f(a+b) + (b-c)f(b+c) + (c-a)f(c+a) = 0
$$
for all $a, b, c \in \mathbb{R}$.
$$
(a-b)f(a+b) + (b-c)f(b+c) + (c-a)f(c+a) = 0
$$
for all $a, b, c \in \mathbb{R}$.
MathNet 2017-part-04 — 176 problems (EN–VI) Question 18
Math Olympiad Vault · MathNet 2017-part-04 — 176 problems (EN–VI)