MathNet 2026 — Part 04 Question 52

Let $p \geqslant 3$ a prime number. For $k \in \mathbb{N}$ checking $1 \leqslant k \leqslant p-1$, the number of $kp+1$ dividers that are strictly between $k$ and $p$ is noted $a_k$. What is $a_1+a_2+\ldots+a_{p-1}$ worth?