Question 12
The real numbers $a$, $b$, $c$ are such that $a^{2} + b^{2} = 2c^{2}$, and also such that $a \neq b$, $c \neq -a$, $c \neq -b$. Show that
$$
\frac{(a+b+2c)\left(2a^{2}-b^{2}-c^{2}\right)}{(a-b)(a+c)(b+c)}
$$
is an integer.
$$
\frac{(a+b+2c)\left(2a^{2}-b^{2}-c^{2}\right)}{(a-b)(a+c)(b+c)}
$$
is an integer.