Question 75
It is given that integers $a$, $b$ and $c$ satisfy the equality $a + b + c = 0$. Denote $S = ab + bc + ca$, $A = a^2 + a + 1$, $B = b^2 + b + 1$ and $C = c^2 + c + 1$.
Prove that the number $(S + A)(S + B)(S + C)$ is the square of an integer.
Prove that the number $(S + A)(S + B)(S + C)$ is the square of an integer.