JMO 1998 Problem 1

Let $p \geq 3$ be a prime, and let $p$ points $A_{0}, \ldots, A_{p-1}$ lie on a circle in that order. Above the point $A_{1+\cdots+k-1}$ we write the number $k$ for $k=1, \ldots, p$ (so $1$ is written above $A_{0}$). How many points have at least one number written above them?