Question 67
Let $a$, $b$, $p$, $q$ be positive integers such that $a$ and $b$ are relatively prime, $ab$ is even and $p, q \geq 3$. Prove that
$$
2 a^{p} b - 2 a b^{q}
$$
cannot be a square of an integer number.
$$
2 a^{p} b - 2 a b^{q}
$$
cannot be a square of an integer number.