Question 125
The positive integers $a$, $b$ and $c$ satisfy the equality
$$
a^3 b^3 + b^3 c^3 + c^3 a^3 = abc(a^3 + b^3 + c^3).
$$
Prove that the product of some two of these numbers is the square of a positive integer.
$$
a^3 b^3 + b^3 c^3 + c^3 a^3 = abc(a^3 + b^3 + c^3).
$$
Prove that the product of some two of these numbers is the square of a positive integer.