MathNet 2024-part-05 — 168 problems (EN–VI) Question 44

Show that there exists a positive integer $K$ satisfying the following: for any prime $p \gt K$, the number of integers $1 \le a \le p$ such that $a^{p-1} - 1$ is divisible by $p^2$ is less than or equal to $\frac{p}{2^{2024}}$.