Question 109
A positive integer $n$ is called *unfortunate* if it cant be represented in a form $n = \frac{x^2 - 1}{y^2 - 1}$, where $x \gt 1$, $y \gt 1$ are integers. Determine whether the set of all unfortunate positive integers is ultimate or infinite. Let's call the natural number $n$ unsuccessful if it cannot be represented as $n = \frac{x^2 - 1}{y^2 - 1}$ with natural $x, y \gt 1$. Sure or infinite number of unsuccessful numbers? (V. Senders)