Question 175
Positive integers $a$, $b$ and $c$ satisfy the equality
$$
\frac{a^2 - a - c}{b} + \frac{b^2 - b - c}{a} = a + b + 2.
$$
Prove that $a + b + c$ is a square of a positive integer.
$$
\frac{a^2 - a - c}{b} + \frac{b^2 - b - c}{a} = a + b + 2.
$$
Prove that $a + b + c$ is a square of a positive integer.