Question 116
Real numbers $a$, $b$ and $c$ satisfy the conditions
$$
(a + b)(b + c)(c + a) = abc, \\
(a^3 + b^3)(b^3 + c^3)(c^3 + a^3) = a^3b^3c^3.
$$
Prove that $abc = 0$.
$$
(a + b)(b + c)(c + a) = abc, \\
(a^3 + b^3)(b^3 + c^3)(c^3 + a^3) = a^3b^3c^3.
$$
Prove that $abc = 0$.