Question 192
Let $a$, $b$, $n$ be positive integers such that
$$
\frac{1}{a} + \frac{1}{b} + \frac{n}{\text{lcm}(a, b)} = \frac{1}{\gcd(a, b)}
$$
(i) Prove that $n$ is odd;
(ii) Find all the possible values of $a$ and $b$ if $n = 2007$.
$$
\frac{1}{a} + \frac{1}{b} + \frac{n}{\text{lcm}(a, b)} = \frac{1}{\gcd(a, b)}
$$
(i) Prove that $n$ is odd;
(ii) Find all the possible values of $a$ and $b$ if $n = 2007$.