Question 32
Let $a$, $b$ be positive integers such that the number
$$
\frac{(a+b)^2 + 4a}{ab}
$$
is an integer. Assume that $b$ is odd. Prove that $a$ is a perfect square.
$$
\frac{(a+b)^2 + 4a}{ab}
$$
is an integer. Assume that $b$ is odd. Prove that $a$ is a perfect square.