Question 129
Prove that there exists integer $n \ge 1$, such that the number of the pairs $(a, b)$ of positive integers satisfying the equation
$$
\frac{1}{a-b} - \frac{1}{a} + \frac{1}{b} = \frac{1}{n}
$$
is greater than 2024.
$$
\frac{1}{a-b} - \frac{1}{a} + \frac{1}{b} = \frac{1}{n}
$$
is greater than 2024.